The responses so far have avoided the issue of whether ones sense of balance gets worse with age. Of course it does, but, that said, that doesn't mean one can't still do (some of) the things we used to take for granted, albeit with more effort, concentration, and practice. My son taught me to ride no-handed again last year (at age 64), but it took a lot more concentration than I remember from my teenage years. Now I make sure I have a no-handed session each time I ride.

I do repair bikes at a local thrift shop, riding each one briefly, and I find that I can ride every one of them no-handed. My take is that the ability to ride no-handed is more physiological and perhaps mental than bike specific.

Jim