The mouse definitely still works, because if I go to the far bottom-right corner and then back one pixel (WTF?), then the "exit" button highlights. Yay.

If you turn off "Fast Cursor" in the game options, do you see the mouse in battle mode? If I recall, that toggle only works when you're fighting, so you might have to toggle fullscreen from inside a battle.

Once the mouse cursor disappeared I wasn't able to do anything, not even changing any other option. That's because the game menus completely lack keyboard controls, and alt-enter doesn't toggle fullscreen like it should. So I just stopped playing.

I didn't come back until today where I wasted enough time blindly moving the mouse and was able to disable fullscreen. I'm never trying anything that might lose me the mouse again, thank you very much.

In future games I suggest you at least support alt-enter, if not actual keyboard controls.