I had my bat pet with me in a dungeon, and as it was fleeing off-screen due to its low health, it somehow sustained a hit while in the area bordering the screen, and then died. Since it was in the area bordering the screen, I could not physically reach it to revive it. I'm not sure if there would be a way to work around this somehow. I could imagine that perhaps the same thing could happen if the bat was in the middle of a large block area on screen (such as a couple large adjacent boulders) that the player could not reach.
Yes, unfortunately this can happen right now. I've raised a bug: http://bugs.bytten-studio.com/bug-114