not all boats are this way, but my hour meter is on an oil pressure switch so if the key is left on for some reason, it doesnt rack up engine hours on the meter....
if yours is set up that way, it could be a faulty pressure switch.... but you can hook the meter directly to a battery to see if its a failed meter...
I have also seen hour meters that ran off the alternator, so when the engine is stopped, so is the meter.