Why didn't Lord Voldemort just keep the Horcruxes in his robes and with him all the time? So no one would dare try and steal from him. He kept Nagini close with him and it turned out to be very difficult to kill the snake.
Simple Answer: If they were on Voldemort and he was killed all of the Horcrux would be left in a pile upon where his body fell. From there it would be very easy to destroy them.
Even if he got stunned or anything that made him temporarily vulnerable specially when Dumbledore was alive.
He could also be attacked by FiendFyre and they would all be destroyed instantly.
Slightly more expansive:
Voldemort assumed himself to be the most knowledgeable wizard of his time going where no dark wizard had gone before. (Star Trek Voldemort). He never thought anyone would know of Horcrux magic nor did he think anyone knew about his hiding places or how to get past the protections. He certainly took pride in the objects that he chose to create Horcruxes with, the treasures of the four houses of Hogwarts. His pride was his downfall ultimately in the end and the beginning.
Think of Horcruxes as some kind of anchors, that keep you in the realm of the living. Then you can think of it even as in world of physics (bit clumsy, but). You are chained to many different places/objects which are far from each other, but the bond with you is very strong, therefore you are very well stabilized. Also, the Horcruxes (at least in Voldemort's case) are not just lying around on the ground (apart from the Diadem, but it was at extraordinary place, at least from Voldemort thought).
- the lake inside of the Cave was very well protected after all:
“The protection was... after all... well-designed,” said Dumbledore faintly. “One alone could not have done it... You did well, very well, Harry....”
- Helga Hufflepuff's Cup at Gringotts:
‘Yeah – so yeh’d be mad ter try an’ rob it, I’ll tell yeh that. Never mess with goblins, Harry. Gringotts is the safest place in the world fer anything yeh want ter keep safe – ’cept maybe Hogwarts. As a matter o’ fact,
Although Hogwarts was safe mostly because of Dumbledore, kinda ironic, that Voldemort used that place (of course, he put it there as Hogwarts is the place that made him extraordinary)
Let's quote Slughorn from his own memory:
Then, even if one’s body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged.
Voldemort never meant to let anybody know about his intentions of creating Horcruxes - asking Slughorn was necessarily for obtaining the information about making more than one. I still think, that one of the strongest defense of a Horcrux is the fact, that nobody knows about it.
“But don’t you see, Harry, that if he intended the diary to be passed to, or planted on, some future Hogwarts student, he was being remarkably blasé about that precious fragment of his soul concealed within it. The point of a Horcrux is, as Professor Slughorn explained, to keep part of the self hidden and safe, not to fling it into somebody else’s path and run the risk that they might destroy it — as indeed happened: That particular fragment of soul is no more; you saw to that. “The careless way in which Voldemort regarded this Horcrux seemed most ominous to me. It suggested that he must have made — or been planning to make — more Horcruxes, so that the loss of his first would not be so detrimental. I did not wish to be- lieve it, but nothing else seemed to make sense.
It is clear, that the person, who created Horcruxes still can be damaged or almost destroyed - therefore unable to protect the Horcruxes anymore, but at that state there are the only things, which held him alive. So, yes there is a plenty of risk involved in hiding them, but it is rather dangerous for the person to keep them with him.
Keeping the Horcruxes with him means they’d all be in one place.
If the Dark Lord kept all the Horcruxes with him, then it would be much easier for his enemies to find them. As he’d done it, first his enemies would have to find his Horcruxes before they could destroy them, and finding one Horcrux didn’t mean they’d be able to find his others. Since he had several hiding places, he increased his chances of at least one of his Horcruxes remaining safe.
“A modicum of calm cooled his rage now: how could the boy know that he had hidden the ring in the Gaunt shack? No one had ever known him to be related to the Gaunts, he had hidden the connection, the killings had never been traced to him: the ring, surely, was safe.
And how could the boy, or anybody else, know about the cave or penetrate its protection? The idea of the locket being stolen was absurd …
As for the school: he alone knew where in Hogwarts he had stowed the Horcrux, because he alone had plumbed the deepest secrets of that place …
And there was still Nagini, who must remain close now, no longer sent to do his bidding, under his protection …”
- Harry Potter and the Deathly Hallows, Chapter 27 (The Final Hiding Place)
If he’d kept them all in the same place, it’d be much easier for someone to possibly find them all.
Also, if his body was destroyed, he won’t be able to retrieve them.
In addition, his Horcruxes were supposed to keep the Dark Lord safe if his body was killed, and keeping them with him would put them in danger should that ever happen. When the Dark Lord was ripped from his body, he then existed in an incorporeal form.
And then he broke: he was nothing, nothing but pain and terror, and he must hide himself, not here in the rubble of the ruined house, where the child was trapped and screaming, but far away … far away …”
- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)
If he’d had his Horcruxes all with him then, they’d all either be left behind in the Potters’ house, or worse, destroyed in the explosion. Even if the Horcruxes survive whatever killed his body, it’d be hard to remove them from the place it was killed, as he’d be in spirit form or possessing animals.