In Empire Strikes Back, Vader nearly kills Luke without hardly seeming to try. Then, in Return of the Jedi, Vader hardly fights at all and he's falling down and then Luke cuts his prosthetic hand off. What happened? How did Vader suddenly become so weak?
Early in the fight, Vader is going very soft on Luke, specifically trying to direct the fight as he wishes.
From the novelization:
Vader was impressed with Luke's speed. Pleased, even. It was a pity, almost, he couldn't let the boy kill the Emperor yet. Luke wasn't ready for that, emotionally. There was still a chance Luke would return to his friends if he destroyed the Emperor now. He needed more extensive tutelage, first --- training by both Vader and Palpatine --- before he'd be ready to assume his place at Vader's right hand, ruling the galaxy.
So Vader had to shepherd the boy through periods like this, stop him from doing damage in the wrong places --- or in the right places prematurely.
But Luke has been training since their last encounter, and the Emperor has been egging him on. Luke is flirting with the Dark Side.
Luke stood above him, at the top of the staircase, heady with his own power. It was in his hands, now, he knew it was: he could take Vader. Take his blade, take his life. Take his place at the Emperor's side. Yes, even that. Luke didn't bury the thought, this time; he gloried in it. He engorged himself with its juices, felt its power tingle his cheeks. It made him feverish, this thought, with lust so overpowering as to totally obliterate other considerations.
It's only then that Vader realizes that he has underestimated Luke.
For the first time, the thought entered Vader's consciousness that his son might best him. He was astounded by the strength --- not to mention the boy's timing, which was honed to a thought's breadth. This was an unexpected circumstance. Unexpected and unwelcome. Vader felt humiliation crawling in on the tail of his first reaction, which was surprise, and his second, which was fear. And then the edge of the humiliation curled up, to reveal bald anger. And now he wanted revenge.
His anger was layered, now --- he did not want to win if the boy was not battling to the fullest. But if winning meant he had to kill a boy who wouldn't fight... then he could do that too. Only he wanted Luke to be aware of those consequences. He wanted Luke to know this was no longer just a game. This was Darkness.
From here on, Vader fights with more skill and ferocity, as one would expect.
I think it has less to do with Vader being weaker and more about Luke being stronger, but I think circumstances play a big part as well. But first, consider this:
Prior to his defeat against Obi Wan
Darth Vader was a formidable fighter. There were not many that would be able to hold their own against him, especially with the Dark Side at his disposal, had he not been forced to wear his clumsy life supporting armor.
Even if he didn't need his suit, he'd still have nobody to fight as the Jedi are thought to be extinct. My point being that lightsaber combat wasn't really a priority for him any more.
Nonetheless, he could easily defeat Luke when Luke was at the beginning of his training, no surprises there.
However, Luke must have been training a lot, and being strong in the Force and with a young healthy body, he would have made excellent progress.
Now, at the beginning of the fight, Luke still has no real chance against Vader, especially since he is more focused on getting Vader back to the light. Since Luke arrived, the Emperor was manipulating him, trying to get him to turn to the Dark Side. This must have been an extremely hard test for Luke, which he alomst, almost, failed.
When Vader mentions Leia, Luke surrenders to the rage. His anger does indeed make him stronger, and he is no longer concerned about turning Vader back to the light. His prior training would be amplified and his only goal is to defeat his opponent. Meanwhile, it is not impossible that Luke actually got through to Vader, which would have had Vader unfocused and confused.
Luke got a sudden huge boost in power, which Vader probably wasn't ready for. This would be especially true if Vader was indeed confused by Luke's earlier persuasion.
Also, note that Luke defeated Vader pretty fast, consider that Vader was able to defend himself for just a little longer. Luke's anger would fade and Vader would get focused. It is very possible that Luke wouldn't be able to defeat Vader if that happened.
See, I've wondered that very thing and here's my conclusion.
Luke's attack came in fierce and violent and initially the attack seemed to catch him (Vader) off guard. If Vader were inexperienced in battle I can see him not recovering. Vader, though, is strong and well trained in the Force, reputed to be a great Lightsaber duelist, and a battle tested, battle hardened combat vet.
Though initially being thrown off guard, someone like Vader should be able to recover from the surprise attack. Especially since Luke's attacks were very wild and out of control and missing with the wide swings.
The theory that Vader needed Luke to be ready to kill the Emperor (and please don't think I'm saying you're wrong), seems a bit risky. What if Luke had killed him? My take on it (and I could be wrong) is Vader realized he couldn't bring himself to kill Luke so, facing that possibility, he sacrificed himself.
TLDR: I laid out a long trail of bread crumbs to show that Vader was actually a lot weaker than we thought throughout the series due to age/injuries sustained as others pointed out. It was just never brought to light until Vader fought with the internal conflict of light vs dark and fighting his son who had been training hard with yoda. There never was any REAL test until the last fight where he went against someone who was actually trained.
I seem to be a few years too late to reply to this but going to add in my 2 cents and hopefully add a different angle. I see a lot of people commenting about how Vader was a great warrior, should have recovered faster or was holding himself back, or even the comment about sacrificing himself.
I think that most of the replies are missing the big key to this though. As some of the other comments pointed out... it's been a LONG time since vader fought. Mostly settling into the role of crazy-old-sorcerer who used force powers to make his men work and little usage of his lightsaber. Due to this, he has had very little training in a more clumsy body. He is use to a light agile body that reacts as he wants.
The duel between him and obi-wan was really hardly a fight, both old and tired, both just swung their light sabers with barely any body movement in terms of moving with the attacks. They attacked some, talked some, attacked some and then obi-wan let vader kill him.
When Vader meets up with Luke for the first time in Empire Strikes Back, Luke had barely any training. Most of it was yoda teaching him to have mental endurance and learn self control but little ability to actually wield a saber. Even in this fight, vader still BARELY fights him with his saber but resorts to force powers and throwing objects at Luke to wear him down. Even in the carbon chamber, there was hardly any actual fighting as Luke spent most of it evading a few attacks. By time they actually started to do any light saber fighting, Luke was already worn down by all the objects thrown at him and lost his arm.
In return of the jedi, Vader already showed signs of weakness from the start. Contemplating and focused on his son. You can see that something was tearing him apart mostly likely due to the thoughts that his son was ACTUALLY alive and well after 20 years of believing that he killed his child before birth. This is going to force a lot of mental strain after years of more than likely self inflicted mental abuse. Luke lands the invisible poison dagger on Vader when they are Endor declaring to vader that his father is truly dead before being brought back to the death star. Vader hangs back and sits on the railing showing signs that the words Luke just stated made him appear to reconsider his life purpose.
By time the actual duel with Luke happens on the death star, Vader is already under extreme mental strain from being rejected by his own child. During this fight, there was no force usage. There was no stand and fight with wet noodles like he did with obi-wan. He was now fighting a trained jedi and having to move, having to think. In his first taste of the dark side, the emperor goads luke into exploiting his anger as he attacks vader making him fall down the stairs but realizes he is attacking out of anger and calms himself down again giving vader the chance to recover as he turned off his light saber. When Vader resorted to black mail and bring up leia, he more than likely expected Luke to collapse in fear and grovel. Luke has been previously reluctant to fight Vader almost avoiding any confrontation and hiding behind props. As others pointed out, the mention of Leia actually snapped Luke into fighting to protect what he considered now to be his only family left. Turning to the dark emotions of anger, Luke attacked Vader with such speed and power and this time, never gave vader a chance to catch his balance and thus the duel was finished quickly as Luke used his anger to cut off his fathers arm and at this point, the sheer power of the attacks from luke using the darkside just overwhelmed vader.
The Emperor also could have sensed Luke's greater potential as a flunky and was already planning to throw Vader under the bus.
So Luke, without knowing it, was getting a force boost from the guy watching all of this, giving Luke an extra edge he otherwise would not have had.