I don't know exactly how it works, but it is connected to the login / return to the game system, if you log in among monsters even without invisibility, you get a few seconds of invincibility(monsters dont see or target you) unless you move, after logging in, in. I think battle status are always appears, appears when monsters are on the screen, but if you are invisible and you don't move, it disappears after a few seconds and not after a minute like normal battle status.