If it gets worse, you probably have damaged tinsel leads or a damaged voicecoil. If it doesn't get worse you probably have an alternator that can't put out enough juice for the amp.
make sure the ground wire in still tightly intact while the subs are doing its thang it could be loosening up the ground wire and that would make the subs cut out and not make the amp go into protect mode
Sounds like a voltage/ground problem. Test the power wire during heavy play and read the voltage. Also re-check all of the connections. And make sure the wire guage and fuse are proper size.