I know this is a bit of an old question, but as I've just finished DH (Harry Potter and the Deathly Hallows), perhaps I can add something.
Here are a few things to consider - and it's possible that any or all of them were at play.
They panicked
DVK has already covered this a little bit in a former answer. It's always worth remembering, when considering perceived plotholes, that the characters are human beings and human beings make mistakes. Lots. Especially when under pressure.
Now, having said that, it's obviously not good enough to just wave aside bad writing and poor plots by going: "ah, humans make mistakes," whenever a character does something that doesn't make sense (or fails to do something they obviously should have done). There's nothing wrong with reading a story and finding an element of the plot unsatisfying for you.
But remember that you are reading the book in the comfort of your armchair, with a mug of tea on the side and all the time in the world to think about what they should have done. Almost every accident in the world, and every blunder ever made, could have been avoided. It's very easy to think: "here's what they should have done - it's what I'd've done" when you read about them in your living room. When it's a matter of life and death, and you're actually in those situations, mistakes happen all too easily. Things get overlooked.
So I think, in general, it's always worth reminding yourself that, in reality, people screw up a lot. Similarly, it's worth remembering how unrealistic it would be if characters in books and movies never made dumb mistakes under pressure. In some ways, I think we occasionally expect too much from characters in stories - that they should never make a stupid move, because that would seem like a plothole.
However, this is a much larger discussion for another place and, of course, if characters make too many mistakes, or the mistakes are too big, then that will make for a very unsatisfying story. Different people will also draw the line in different places. One person might be satisfied with the explanation: "well, they were under pressure, they made a mistake," in this case; whereas you might simply be unable to believe that all three of them could overlook such an obvious escape route.
Anyway, as an important subpoint, I want to draw your attention to one thing that I think makes this mistake very believable. They essentially had guns pointed at their heads (the equivalent). And when people have guns pointed at their heads, they freeze. It's instinct. The risks of trying to escape are too high. Even in situations where escape is actually probably quite possible, most people won't dare run when a weapon is pointed at them.
Now, of course, the Snatchers arrived outside the tent, there was an opportunity for them to flee. Hermione also had time to perform a spell on Harry. However, I think there's a good chance instinct would have kept them from risking it. If they messed up, they risked being killed simply because they attempted to flee. It's also not clear how far apart they are, but if they're too slow they also risk being hit.
Time
A related point to consider is that everything actually happened very quickly indeed. Ron's immediate reaction - rightly or wrongly - is to try and put the defences back up. This is understandable, even if he may have been better off attempting to flee with the others immediately. Remember also that Ron seems to be the one most acutely aware of the Taboo. Harry and Hermione are probably still processing what's happened when the Sneakoscope goes off.
From that point on, this is what happens:
But Ron stopped talking, and Harry knew why. The Sneakoscope on the table had lit up and begun to spin; they could hear voices coming nearer and nearer: rough, excited voices. Ron pulled the Deluminator out of his pocket and clicked it: their lamps went out.
'Come out of there with your hands up!' came a rasping voice through the darkness. 'We know you're in there! You've got half a dozen wands pointing at you and we don't care who we curse!'
Harry looked round at the other two, now mere outlines in the darkness. He saw Hermione point her wand, not towards the outside, but into his face; there was a bang, a burst of white light, and he buckled in agony, unable to see. He could feel his face swelling rapidly under his hands, as heavy footfalls surrounded him.
Harry Potter and the Deathly Hallows - pp.360-2 - Bloomsbury - chapters 22-3, The Deathly Hallows and Malfoy Manor
It's impossible to be sure, but it sounds like they had all of about 10 seconds.
The tent and the sword
In the tent were all their worldly possessions, including - most importantly - the sword of Godric Gryffindor - their one precious weapon against the Horcruxes. We don't know exactly where the sword of Gryffindor was, but we know that shortly before they were caught, Hermione had been polishing it idly. Nothing more is said about it and we can assume it was left lying around:
Roused for the first time in days from his contemplation of the Deathly Hallows, Harry hurried back inside the tent to find Ron and Hermione kneeling on the floor beside the little radio. Hermione, who had been polishing the sword of Gryffindor just for something to do, was sitting open-mouthed, staring at the tiny speaker, from where a most familiar voice was issuing.
Harry Potter and the Deathly Hallows - p.355 - Bloomsbury - chapter 22, The Deathly Hallows
It seems reasonable to me to assume that they would not have been able to grab the sword - or anything else vital - in time, especially when Ron has just extinguished their lights.
If they lose the sword of Gryffindor they lose a lot. I would also like to stress again that, in situations like that, you don't have time to objectively weigh various factors. Tiny little influences in your subconscious will tend to dictate your thoughts and actions and responses. It's possible that the pull of their "base" - and its precious contents - exerted a powerful influence on them and kept them from fleeing at once.
They underestimated the threat
This is an interesting one. It is clear that they know that breaking the Taboo can be dangerous:
'...They nearly got Kingsley-'
'You're kidding?'
'Yeah, a bunch of Death Eaters cornered him, Bill said, but he fought his way out.'
Harry Potter and the Deathly Hallows - p.316 - Bloomsbury - chapter 20, Xenophilius Lovegood
And it's clear that they fear the Snatchers:
'Some of them are supposed to be as bad as Death Eaters,' said Ron.
Harry Potter and the Deathly Hallows - pp.354-5 - Bloomsbury - chapter 22, The Deathly Hallows
However, Ron's already got away from Snatchers once and, in his one experience of them, they were pretty rubbish:
'The lot that got me were a bit pathetic, but Bill reckons some of the are really dangerous.'
Harry Potter and the Deathly Hallows - p.355 - Bloomsbury - chapter 22, The Deathly Hallows
This one's open to debate, but I think there's a chance they just didn't anticipate how much trouble they were in and expected that their various disguises and alibis would be enough for them to talk their way out of trouble. Or fight their way out of trouble like Ron did before.
Also, again, subtle influences. Is it worth abandoning the precious sword of Gryffindor for a bunch of morons who can be fooled by a false name? You have hindsight, you know how much trouble they were in. They may not have done. Yet.
Anti-disapparition
This, I think, is perhaps the strongest point and there are a few things to say.
It is, I suppose, possible that the Snatchers may have cast some kind of Anti-Disapparition Jinx, or that the Taboo itself prevented those who broke it from Disapparating, as Janus opines. However, there's no evidence that that happened and the trio certainly didn't attempt to Disapparate. However, it's possible that they might have assumed that they would be unable to Disapparate and therefore didn't risk it.
Additionally, at this point, we (and, presumably, they) do not know what happens if you try to Disapparate somewhere where you can't Disapparate. In The Half-Blood Prince Wilkie Twycross has this to say:
'...May I emphasise that you will not be able to Apparate outside the walls of this Hall, and that you would be unwise to try.'
Harry Potter and the Half-Blood Prince - p.359 - Bloomsbury - chapter 18, Birthday Surprises
This does make it sound like it would be dangerous or harmful for them to attempt to Disapparate, if an Anti-Disapparition Jinx had been cast. Of course, later in the book, we find that the air seems to become solid and you just can't Disapparate. However, there's a chance that they feared the consequences of attempting to Disapparate.
Personally, I do not favour this explanation, as there's no hint of any such spell being cast and I can't really see all three of them - panicky and under pressure - having had this thought process. Nor do I see any reason why they would assume a certain piece of magic must have been cast.
However, they presumably did cast an Anti-Disapparation Jinx on their own tent, as part of their defensive enchantments.
Now, I can't be sure (I don't think it's confirmed) whether the Taboo breaks the Anti-Disapparition Jinx. The Snatchers were able to Apparate outside the tent - within the confines of the other protective enchantments - but not within the tent itself. Perhaps it was still impossible to Disapparate from that tent - or perhaps the trio assumed it would be.
However, again, I don't favour this explanation as such, it seems unlikely that the Taboo would not break this enchantment.
No, I think the main point is that, until then, the enchantment has always been in place. Until then, it had never been possible to Disapparate in that tent. For weeks and weeks and months and months, Disapparating meant leaving the tent. It was so ingrained in their psyches and under pressure, humans tend to revert to instinct and habit and ingrained rules. Although, of course, this is all very unpredictable and, as I said above, panic can cause you to overlook even basic things that you really should know. Nevertheless, I believe that they were so used to being unable to Disapparate from within that tent that it simply never occurred to them that that had suddenly become an option.
Edited to add:
(A little unfortunately, "Apparition" is the term used both for the generic action, as well as for arriving by Apparition. "Disapparition" is, of course, departing by Apparition. Therefore, from this point on, I will use Apparition to denote the general process and Apparition to denote the specific action of arriving by Apparition. I may fail to be consistent, but I'll do my best.)
In their comment, Janus Bahs Jacquet raises an important point against this theory. They ask why the trio would cast an Anti-Disapparition Jinx, which can only hinder them. At best, it's an inconvenience; at worst, it cuts off their only escape route. Implicitly, Janus is casting doubt on the idea that the trio would have cast an Anti-Disapparition Jinx, which renders one of my explanations a little limp.
Well, it seems pretty clear that, for one reason or another, the trio did prevent Disapparition within their camp. (I give full credit to DavidS for raising this point in his answer). When Ron walks out on the other two, he does not Disapparate immediately, as would seem logical, but - at the very least - leaves the tent first:
"Ron, no - please - come back, come back!"
She was impeded by her own Shield Charm; by the time she had removed it, he had already stormed into the night. Harry stood quite still and silent, listening to her sobbing and calling Ron's name amongst the trees.
After a few minutes she returned, her sopping hair plastered to her face.
"He's g - g - gone! Disapparated!"
Harry Potter and the Deathly Hallows - p.254 - Bloomsbury - chapter 15, The Goblin's Revenge
How could we explain such a thing?
Well, there is little direct canon information that I'm aware of that describes the process of preventing Apparition. In general, where Apparition is prevented, both types are impossible. This is certainly true of Hogwarts (I really hope nobody needs a quote to prove it :P), but it also appears to be true of the Burrow. When Rufus Scrimgeour arrives unannounced at Harry's birthday party in The Deathly Hallows, Tonks and Lupin decide they'd better leave:
He seized Tonks's wrist and pulled her away; they reached the fence, climbed over it and vanished from sight.
Harry Potter and the Deathly Hallows - p.103 - Bloomsbury - chapter 7, The Will of Albus Dumbledore
Similarly, when Harry arrives at the Burrow in The Half-Blood Prince:
Tonks hurried past Dumbledore and Harry into the yard; a few paces beyond the doorstep, she turned on the spot and vanished into thin air.
...
[Dumbledore] made Mrs Weasley a bow and followed Tonks, vanishing at precisely the same spot.
Harry Potter and the Half-Blood Prince - p.82 - Bloomsbury - chapter 5, An Excess of Phlegm
We might very well ask the same question, surely? Why would the Weasleys feel the need to keep themselves from Disapparating from their home? Indeed, it momentarily exposes them to danger, surely? At Hogwarts, it makes sense to explicitly prevent both - what with many kids likely to be up to high jinks - but I'm not sure that's such a cogent argument in a family home. Perhaps with Fred and George...But Fred and George have left home by The Half-Blood Prince and have long since passed their Apparition tests. I'd've thought it'd be worth disabling that little enchantment if it were possible.
In any case, something that I find very telling is that after Kingsley's Patronus arrives at the wedding, informing everyone of the fall of the Ministry, people Disapparate and this is taken as evidence that the defensive spells have broken:
Guests were sprinting in all directions; many were Disapparating; the protective enchantments around The Burrow had broken.
Harry Potter and the Deathly Hallows - p.134 - Bloomsbury - chapter 9, A Place to Hide
Even more importantly, it is also impossible to Disapparate from Grimmauld Place. Now surely, surely no good can come of that?
Witness Lupin's departure:
'Remus, Remus, come back!' Hermione cried, but Lupin did not respond. A moment later they heard the front door slam.
Harry Potter and the Deathly Hallows - p.176 - Bloomsbury - chapter 11, The Bribe
And, most importantly, the trio's departure for the Ministry:
They made their way on to the front step with immense caution: they could see a couple of puffy-eyed Death Eaters watching the house from across the misty square. Hermione Disapparated with Ron first, then came back for Harry.
Harry Potter and the Deathly Hallows - p.194 - Bloomsbury - chapter 12, Magic is Might
That said, it's interesting to note that, in The Order of the Phoenix, Fred and George freely Apparate all over the house. Perhaps the Order felt the Fidelius Charm was enough at that point and Apparition was prevented later - perhaps after Dumbledore's death? Hard to say, and I haven't the time to go through the books with a fine-toothed comb looking for additional details.
One way or another, I get the distinct impression that one usually prevents Apparition generally - both types - and not Apparition specifically. Again, very little is said about this. In The Half-Blood Prince we have the following exchange:
'Professor, why couldn't we just Apparate directly into your old colleague's house?'
'Because it would be quite as rude as kicking down the front door,' said Dumbledore. 'Courtesy dictates that we offer fellow wizards the opportunity of denying us entry. In any case, most wizarding dwellings are magically protected from unwanted Apparators. At Hogwarts, for instance -'
'- you can't Apparate anywhere inside the buildings or grounds,' said Harry quickly. 'Hermione Granger told me.'
'And she is quite right. We turn left again.'
Harry Potter and the Half-Blood Prince - p.62 - Bloomsbury - chapter 4, Horace Slughorn
And that's about the extent of it, unless I've forgotten something important.
On the other hand, twice it appears that Disapparition specifically is prevented.
When the trio arrive in Hogsmeade towards the end of The Deathly Hallows, they arrive by Apparition:
Harry pulled the Cloak down as far as it would go, and together they turned on the spot into the crushing darkness.
Harry's feet touched road. He saw the achingly familiar Hogsmeade High Street...
Harry Potter and the Deathly Hallows - pp.446-7 - Bloomsbury - chapters 27-8, The Final Hiding Place and The Missing Mirror
However, they cannot Disapparate:
'We're going to have to try to Disapparate, Harry!' Hermione whispered.
Even as she said it, he felt the unnatural cold begin to steal over the street. Light was sucked from the environment right up to the stars, which vanished. In the pitch blackness, he felt Hermione take hold of his arm and together, they turned on the spot.
The air through which they needed to move seemed to have become solid: they could not Disapparate; the Death Eaters had cast their charms well.
Harry Potter and the Deathly Hallows - p.448 - Bloomsbury - chapter 28, The Missing Mirror
Secondly, at the end of The Order of the Phoenix, Dumbledore mentions an Anti-Disapparition Jinx specifically:
'If you proceed downstairs into the Department of Mysteries, Cornelius,' said Dumbledore ... 'you will find several escaped Death Eaters contained in the Death Chamber, bound by an Anti-Disapparition Jinx and awaiting your decision as to what to do with them.'
Harry Potter and the Order of the Phoenix - p.721 - Bloomsbury - chapter 36, The Only One He Ever Feared
For what it's worth, on balance, I believe that there is likely to be some kind of protective enchantment that can be placed on a dwelling preventing Apparition - both types. This has the character of a safety and security measure. I imagine there is also a means of specifically preventing Disapparition, as a means of preventing escape. This has the character of a Jinx. It may even be moderately advanced magic and it's arguably offensive. The trio may have been unaware of it. They certainly wouldn't have desired to use it.
It is, however, possible that there exist separate measures to prevent Apparition individually and Disapparition individually.
It may be that there is a generic enchantment preventing Apparition - both types - and then an enchantment to prevent Apparition specifically and one to prevent Disapparition specifically. If this is true, it is possible that the trio only knew of the generic form - in which case, fair enough. If they had ever come across a means of preventing Apparition specifically, it was certainly an oversight not to use that and only that, I would say.
It may also be that there only exist enchantments to prevent Apparition specifically and Disapparition specifically. In this case, it certainly seems downright bizarre that they consciously chose to prevent Disapparition. However, canon evidence suggests that's what they did.
My response would simply be: I am not a wizard, I have not done seven years at Hogwarts, I don't know much about spell-casting; but it seems that, for one reason or another, they cast enchantments preventing Disapparition. Hence everything that follows from that in my answer.
However, the canon sources I quoted above aside (and even with them in mind, to some extent), I can understand someone doubting that they would have made Disapparating from that tent impossible. In which case, I would have to lean on my previous points. Although there is perhaps a tiny dribble of cogency left in the idea that the leaving process that had been ingrained in them required leaving the tent.
