The most worrying thing about this thread is only one person mentioned in it is older than me, and he's someone's dad. Anyway, there's no upper limit to enjoying the game but I think there's an age - probably between 12 and 17 - where it's most difficult because you're going to have the piss ripped out of you something rotten by your friends, and at that age you will probaby have more difficulty dealing with the peer pressure thing. Once you're past 17, 18, you're in that bracket where you'll revel in anything that makes you different, and then once you're into your twenties you're properly your own person and you'll do what you like without worrying what people think.
Apart from arthritis, the only other limiting factor is that once you pass a certain age it gets difficult to remember the 400-odd pokemon, all the types and their weaknesses and strengths, the moves, the HMs, egg groups, natures, berries etc etc - you'll just sit in a chair with a blanket on your lap rocking back and forth muttering "Bulbasaur" to yourself while a nurse changes your bag and feeds diamorphine into your drip.
and your never to old toplay pokemon. but if you between 60 and 99 your way too old.