Unless it was installed incorrectly then I doubt it the battery or alternator. I had 1400wrms of bass and 600wrms of speakers running off a stock 100amp alternator and Bosch Gold battery and it would handle it fine, on extreme bass notes it would drop as low as 11 volts but it would never cut out.
Here are some possible solutions
1. Gain is too high, basically you are over-driving your sub amp and sending it into protect.
2. The amp is overheating and going into protect mode. To test this, run this at the same settings it cut off last time and then feel the amp, if it burns you then its too hot.
Is there a main power cable going to the backseat/boot and then using a distribution block to go to all your amps, if so then check the wire from the block to your amp, it should be at least 4 gauge. Also check the ground wire is tightened properly on both ends.
If you have had the gear installed recently then go speak to the installer.