Look at the voltage between the amplifier positive terminal and the case and observe as the amp cuts out.

Does it drop substantially?

No... move on to something else

yes... check this...
Check for voltage between the metal casing of the amp and another grounded exposed body part with such as the door jamb catch, preferably with a needle type volt meter on 2v range, but digital will do.

Make sure you have the meter connected well by checking that that it reads 0v. Bump the system nearly or until it cuts out. It should remain within a fraction of one volt.

If this jumps with sound, you have a poor ground connection between the car and the amp.

yes.. loose ground
no.. loose positive ground