Completely anecdotal, but I've tried chessboxing (as an amateur) a number of times. I'm an awful, awful chess player but a decent boxer and I'm reasonably fit.

Personally I've found some sort of link between mental and physical exhaustion, though I'm not sure which causes which.

I think that being struck in the head probably leads to a loss of control and an overall inability to remain cool more than it affects mental capacity. People panic when someone's trying to punch them. That said, the more experienced (and physically fit) a boxer, the longer they can last before becoming overwhelmed. I don't think it's as simple as purely a mechanical reaction to being punched in the head.