The body is not designed to keep effort going at all costs. You will be informed when you have a cramp, because you should slow down and wait it out before continuing. The whole point of pain is to react to broken stuff, usually by stopping using it.
It will however keep life going at all costs, sometimes digesting replaceable muscles into energy for non-replaceable elements. But it's more about starvation resistance than about chasing. It could also be the case if we were a specie of static filter feeders
A lot of the human body has been affected by long walks and runs, and we do have (well, not me in particular) over-average stamina developped presumably for hunting. It's just the specific exemple of muscle digestion that I'm going after here
this knowledge comes from, uh... idk :3