The problem is likely caused by a worn potentiometer used for bass control on the head unit. They can wear out. Does the bass control **** feel smooth or gritty/loose when turned? If it is not smooth and the bass cuts in/out when turning it, the contact points are likely worn and have intermittent resistance. You can take it apart and test resistance with a meter. You may be able to swap parts from a head unit that is in better condition, but that is hit or miss. The controls are on a separate circuit with small connector. Or find a new replacement part based on orig. specs. and solder it in. If its a Pioneer, you may be able to source the part from them with the service manual to identify part number. If Nakamichi, parts no longer available - you may need to order from electronics supplier like Digikey or Mouser. There are a few places that will service these units if you are not DIY, but it is expensive.
Also, you can disconnect the subwoofer connector and test it individually. It would be very rare, but a speaker's voicecoil can have an intermittent open circuit scenario, when it heats up and expands. The amp can have problems too, but it is not as likely to be the cause.
Have you removed the subwoofer grille cover on the parcel shelf to inspect the subwoofer condition? Is the surround in good shape?
Last edited by Schramm; 07-07-14 at 12:10 PM.