Trout is exactly right. I'd go so far as to say you probably have thin foil duct on back, causing the problem. I made a few tips you can read here
on the way to vent a Maytag.
Additionally, the stopping is an indication that certain bearing swelling has occurred in the motor, which has its own internal overload. I am letting you know that even if you correct your vent and have it cleaned, the motor may still persist in shutting off. Just prepare yourself for the eventuality of changing the motor.