My instructor is 62 and isn't as fast as he was in his 30's when I started training with him, but he is still fast and he is still able to get blinding speed on many techniques. If anything, he is more powerful now than he was back in the day. The amount of power he gets from being able to mobilize his mass is amazing. He also has the annoying ability to be able to control the distance when sparring so that he can literally just be right at the edge of your range so you're unable to hit him with anything and then move in a clobber you. He can also read body language so well that he can tell what kind of techniques you're getting ready to throw (this is something that is an often overlooked benefit of step-sparring, IMNSHO) which means he's already getting ready to defend against the technique as soon as he sees you move.
These are all abilities of his that I've seen develop over the past twenty five years. He had them all when I started training but they've simply increased over time. In some ways he's a better fighter now than he was then. Consistent smart training is the key. If you get injured take an adequate amount of time to rest up before returning to training. Keep yourself well hydrated when training. Remember that Taekwon-Do techniques, when done correctly, shouldn't hurt. If you're hyper-extending your joints you're doing it wrong!
Pax,
Chris