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:
But Luke has been training since their last encounter, and the Emperor has been egging him on. Luke is flirting with the Dark Side.
It's only then that Vader realizes that he has underestimated Luke.
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:
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.