Since the music is going off too the problem isn't the mic.
Your mixer/amp/speakers may have a problem. As suggested above If the amp is overheating then that would also shut it down. It would come on again after it cooled off. It would go off again when it got hot. If you have a bad speaker that could cause it to shut down too but it would be less likely to cycle off and on. If you have more than one speaker than disconnect each on to see if the problem goes away.