Why did Vader keep falling down when battling Luke on Cloud City and on the second Death Star? In Cloud City when he falls off the ledge when he and Luke are battling on top of the carbon freezing platform, when Luck backs him up, and when Luke kicks him on the second Death Star? Was Luke that much better or did it have to to with Vaders mechanical parts?
On Cloud City, Vader is holding back. Luke is his son. He can easily whip him, but his intent is not to win the fight. He wants to test Luke to find out if he's worthy of being turned. Vader wants to push him, tire him, taunt him, leave him mentally and physically exhausted so he can turn him.
I've always gotten the impression that Vader underestimates Luke in the Cloud City fight and is occasionally surprised, like when he takes a graze on the shoulder. Vader thinks all the training Luke got was from Obi Wan who's been dead for years, he doesn't know about Yoda's training. As for the first kick off the platform, I think Vader set it up. He leads Luke into the fun house below where he can surprise him, confuse him and batter him.
The battle on the Second Death Star is a similar matter, but things have changed. Vader and the Emperor are playing the same game, they're not trying to kill Luke, they're trying to break him and turn him. Vader still has to hold back, but something more. Luke is still Vader's son, and they've had a little heart-to-heart on Endor, so his heart is not entirely in it. Luke is much stronger now, and Vader can't play Luke like he did in Cloud City.