Personally, I think the lack of stamina that comes with age has little to do with it - particularly thinking of Paul Strand, whose later work, for me, is his best.
Not mentioned much on the blog, but how productive we are at any given age surely has a great deal to do with external influences - the people you come into contact with, how inspired you are by your environment, MONEY! Living a life of uninhibited experience might be the most important factor in producing great creative work. Four walls in a one horse town don't stay inspiring for long.
I've decided to substitute 'influential' for 'best', since there are plenty of photographers working on the fringes, producing great work - and by that, I don't mean the guy you know from the local gallery, but photographers with status, who seem to have little impact on other photographers. Thomas Joshua Cooper is one of my favorite oddities, in that I've never seen any real reference to or imitation of his work. Same with John Blakemore - who incidentally, produced his most notable pictures on his kitchen table in his later years. You can tell by now, I'm trying to keep some of the older guys here a little hopeful!
Thinking of my own demographic, Stephen Shore produced a lot of his work for Uncommon Places at 26. Lewis Baltz started his Prototype Works at 24. The funny one Soth mentions is Lartigue, who hit his peak at 11.
I don't think age should be even considered with regards to art. Latigue produced some of his best images in his teens, others were much older. I do know that any one over 50 is not eligable to enter for the Turner Prize. Why? What would Turner have made of this rule?