Low voltage, thermal, or a combination of both can shut down an amplifier. However, the other amplifiers are not exhibiting the same behavior. And the tower amplifier does not have an inordinately low load or a particularly difficult load. It also seems from your discription that the tower amplifier is turning off too early for a thermal issue. Usually this requires a period of time.
If all the measureables appear to be okay then proceed this way.
Try one tower speaker at a time with the other amplifier terminals disconnected. Then try one speaker on one channel only in the stereo mode rather than bridged.
Trying to find a normal mode of consistent operation is a good start. Then keep adding channels or bridging one side at a time until you see the problem appear again. At that point you have a strong clue.