I can see ma ai in operation in many arts and sports. What they call it in each one I wouldn't know.
Ma-ai equals backed up in an untenable situation? Methinks not. As I said, a rarely emphasized thing. Dare I say commonly misunderstood????? Perish the thought.
"Rarely emphasized?" Well, my current teacher only mentions it a few times a week, but I don't know if you could call that "rare."
In any case, if a person approaches within a distance you find uncomfortable, you don't really have many choices.
You can back up, "maintaining ma ai." Which will eventually put you in a bad position.
You can stand your ground, and take some action to respond to their approach. Which isn't "wrong," but doesn't "maintain ma ai," either.
You might consider the closely related concept of "de ai," the "critical interval." At this distance, the parties are no longer "safe," and are effectively forced to either enter or retreat.
I know you weren't talking about weapons, but weapons provide the simplest illustration. A person is walking toward you with a sword held in seigan stance. There is no overt "attack," they're just walking, but they do have three feet of sharpened steel aimed at your throat. You can't just stand there.
What do you do? You can step back: they follow. You can step to the side: they follow. Or you can enter, and in so doing force them into a reaction.