Does the amp go into protection with source connected or no signal. The 777a is one of those amps where you rarely need the volume past 11, not because it is a power monster, but because potentiometers back then werent logarithmic - so 3 o'clock likely means full power. Even without a signal, I would not be surprised if full power can trigger the protection circuit. It is a very simple system, just consisting of a thyrister with a threshold adjustment determining when DC current fed back from the output emitters are too much. As Skippy124 says, that adjustment can be too trigger happy or there is an actual fault hiding there or somewhere else triggering the protection. However - unless the loudness causes "protecting" from "normal" volumes - then I am not surprised that cranking a 50 year old amp with a simplistic protection circuit can be triggered, signal or not.
If the amp on all other account functions/sounds normally then I would not worry about it - in fact the amp is showing you that its protection is working when maxed out on power. If the switches are very dirty, especially the volume, then they could potentially produce some loud scratchyness that might find its way to a trigger happy protection circuit, this include a dirty loudness switch, so cleaning all controls is a really good idea to do first.
