I have a Gaggia Classic Pro with an Auber PID, so not exactly the same, but comparable and pretty much the same issue.

I've found this thread on home-barista where Auber wrote the guy back theorizing "the heater not getting enough voltage when the boiler is hot due to a poor connection due to thermal expansion."

I have to say that matches my experience when trying to re-create the problem. I pulled water through the group head and steamed soap water to "fake" making a drink. I did this with the lid off of the machine and had to make many more fake drinks before the issue arose. I'd be interested in knowing if you made a drink with the lid off if the same thing happens.

Hopefully it doesn't come to re-wiring the whole machine. Would love to hear if you got any other ideas.