Individual games do. Characters don't. Tifa and Cloud don't age even when you republish Final Fantasy VII decades over. The Toy Story characters and Mickey Mouse are ageless.
Hollywood has the problem that is has to resurrect actors from the dead or painfully de-age them and they still move like old people. It makes the morbid character and false economy of nostalgia very hard to ignore. If animation and game characters had creaky knees and sagging skin because they've been doing the same thing for 40 years maybe we'd let them retire and focus on something new.