I don't know about fighting in particular[1], but in sports, there is a detrimental effect related to age. But it's relatively slight and can be overcome through training.
Generally, older people are more likely to be out of shape because they're more likely to be sedentary. And, of course, if they had a lifetime of bad habits like smoking or drinking, the cumulative effects can be significant.
There's another age-related sports thing -- people who are in professional sports tend to beat up their bodies quite a bit. They age out of their sport, not really directly because of the passing of time as much as because eventually the cumulative damage catches up to them.
[1] That said, I know a couple of people in their mid-60s who could kick the crap out of the majority of 20somethings.
