Two pages without stats???...
Well, this is hardly conclusive, but
HERE are results from a local 5K that seem to show a dropoff around age 35. That seems to connect with my impression of performance of NFL wide receivers, or quarterbacks not named Brett. If running backs or linemen tend to drop off earlier, it's likely more a result of getting clobbered too many times than pure age.
HERE are results from something more my speed, the 24 hour bicycle race at Sebring (here's hoping my name is high up there next year). These results would point to a dropoff much later, around 50 or 55, for long, long endurance events.
Either way, I don't think it would bother me if I was 60+. If you are competitive in your age group, that should be enough. Heck, some don't make it to 60, and many more could hardly ride a bike at all.