Car subwoofer not working properly?

I have a sony xm-2100GTX Xplod amp and a single subwoofer.I still get power on my amp(i thought maybe the amp was dead but the power light is on) My old MA audio subwoofer went to crap so I got a new one after a month i noticed the bass would cut out and come back on. for some reason if it had time to cool it would work for about 30min or so then just cut out. I remove fuses from the amp because it was getting annoying, any suggestions on what might be the issue or how I can resolve it? I also have a Kenwood KDC-138 CD-Receiver. (I barley know how to use x_x) THX