My guess? Its an impedance mismatch on the radio audio output(s). A circuit is 'protecting' itself and cutting the output off to dissipate the heat generated and hopefully protecting the hardware. I would go ahead and try the head unit swap, be careful not to let it continue. It may be the radio, or the wiring after the radio outputs (including the amp and its associated wiring). If the radio swap results in the same thing, your wiring would be highly suspect. I would then look for crossed wiring (chaffed insulation) at both devices (radio/amp) or an open in one or more of the pairs of voice coils to the dual coil speakers. This type of 'protective' circuit is designed to save hardware, so be aware it should not be allowed to continue as each time it happens components may be weakened. Good luck!