If you are using a booster amp you are driving too many amps into the subwoofer, making your amp go into safe mode, you will need to get a subwoofer able to take more amps
Subwoofer Goes Out After Several Minutes Of Play In My Car System. Can You Help?
You should check to see if the amp is turning off. If some amps get to hot it will go into failsafe and turn off.