We tend to think of it as a continuing awareness of our surroundings, and of threats in the environment. It's not just in kata, that just has a specific way of showing it. It's supposed to be everywhere. I've had someone try to mug me when I was sick, exhausted, and in totally the wrong mood for a fight. When he noticed I'd seen him approach, he started to try to talk his way in, and my threat sensors are going off(rather muffled by the sneezing and coughing, but oh well) something fierce. I managed to keep him out of charging range by maneuver, all the while talking back and trying to let him think it was working. Mirroring his affect was a very useful tactic, as it let him think he was controlling me.
1) As soon as I got near the door of my apartment, he realized he wasn't, but it was too late then.
I walked in listening to his screams of "!!!! you, !!!! you, !!!! you!" thinking awww, did poor little baby want to mug me?
I've had juniors whack me some fierce ones, and totally freak out, thinking they'd hurt me. They're standing there with their mouths open doing the usual "Oh, my God, I'm sorry, I didn't mean to...!" If they're really junior I just shrug it off and grin, say you need to hit harder.
2) If they're a bit more senior I point out that they're SUPPOSED to be hurting me and if they lose awareness just by hitting me, then they need to work on that.
If they're 5-3 kyu or higher, I just continue the exercise and attack again. If they can't handle the attack, they need to work on their zanshin, and not be so worried about me. If I'm on the ground unconscious or screaming in pain, they have permission to help me. Otherwise, just get back in position and be ready to continue.