I'm quickly coming up on 40 and I know that I've lost a bit of burst on my first step. I work out more than average folks and do so specifically to strengthen parts of my body needed for tennis. But, facts are facts, and my 40 yd dash time today is not what it was at 22.
Looking around at my tennis buddies, I think 60 is around the age that the majority become a lot slower. Few singles players in that group. They just adapt to the game to compensate for the loss of step. Playing inside the baseline, not fearing no-mans land, half volleys, etc. a lot of these guys are really good doubles players due to their anticipation and reactions rather than foot speed.