I am in the Navy and I think of it like being on the flight deck of an aircraft carrier during flight operations. The flight deck is a dangerous environment. You have all kinds of threats, you can be blown overboard, sucked into an intake, chopped up by an E-2 propellor, walk off the flight deck and fall into the catwalk .... There is a term we use "keep your head on a swivel" because if you are paying too much attention and concentrating on that Hornet that is turning and about to blast you with his jet exhaust you are going to miss the other Hornet that is about to run you over. So that is what you are doing - while you are doing whatever your job is you are at the same time constantly scanning 360 degrees for other "threats". This is a trained behavior, not a natural one.
We are not talking about a duel or gladiator arena, and as such, I would imagine trained fighters in combat are going to do the same thing, constantly search for new threats.