or glossy, or reflective, or whatever you want to call it
it is likely one of two things. either the lock mechanism is broken, or it is corroded/clogged with dirt. It is possible it just needs to be lubricated, but I doubt that
Cleaning the capstan, pinch roller and rubber wheel and play head with denatured alcohol won't hurt a thing and may stop your problem.
You should check once more for a battery. There are very few smoke detectors sold anymore that don't have. It sounds like you were getting a low battery alarm, but steam or dust can trip them as well. If in fact your units don't have battery backup you really should purchase one or two battery types just for the extra security. When a building catches fire the electricity is one of the first things to go.