Hines didn't improve his playing, he just grew another hand.
A lot of pianists seem to improve - or at least not decline - with age. I suppose it's because declining physical strength doesn't affect their playing ability as it does, say, high note trumpeters like Roy Eldridge or Maynard Ferguson, to give pretty obvious examples. Hines and Bill Evans have already been mentioned - I've been listening to some beautiful contemporary stuff by Harold Mabern, Richard Wyands and Kenny Barron, none of them young men any more. And Basie and Ellington were still there right up to the end, as far as I'm aware. It's not a hard and fast rule though - you only have to think of Bud Powell, but then his problem wasn't physical decline.