Altec Lansing Boombox shutting down on Battery

My Altec Lansing Imt810 shuts down when on battery power after 5 - 10 minutes. After that initial start/stop, it can generally be powered back on but will shut down soon afterward. It seems to me like something might be overheating. The batteries are new and from the same package and each has been tested, each carrying a near full charge. The symptoms are the same whether playing the radio or a device.

There is a common problem with this unit that describes similarly, but with the unit plugged into power. I'm having no problem with the unit when it's on AC power.

Does anyone have an idea of where I can start looking for the problem?