Key Found!!! My wife found the key in her make-up case

I'm happy we have it so we don't have to invest in a new one but a bit bitter that I drove for 9 hours with the key on us the whole time.
In retrospect I guess I'm happy we didn't get into the car without the key. I assume the alarm would have sounded if we opened the door and the key wasn't in the trunk. Does anyone know if the alarm 'times out' or would it just drain the battery all the way down?