im sorry to hear that! have you checked out the voltage while all of this is happening? perhaps you have a bad alternator? it shouldnt dip below about 13 volts while the car is idling and should be higher then that while cruising. if the voltage dips too low for too long it will cause all kinds of wackyness in the electrical system.

other than the voltage, it may come down to a process-of-elimintaion. first unhook the inline fuse for the power wire and the RCA wires from the amp in order to isolate it. if that doesnt stop it, try the headunit, and so on.