Hi, I worked on this PS in a 7904 some years ago. There are two overload conditions, over/under voltage and over current. Either shall turn the supply off. However, I think there is a third condition that will turn the regulator off which is not quite obvious. If you have arcing in the multiplier for example you will get sudden and random load changes and thus disturbances that will destroy the phase of the signal coupled to pins 10 and 11. The phase detector will go nuts and the regulator will turn off, I think.
Can you hear a hissing sound, if so it could indicate arcing?
Meanwhile, there are a couple of tests that you can do but it takes some courage. Short pin 2 (FAULT SENSE) and then pin 13 (ISENSE) to ground. If the behaviour remains the same then shut down is not triggered through these ports.
Carry on
G?ran
G?ran Krusell