Sounds like a flaky tape monitor switch. Next time it goes out, switch the monitor in and out a few times, see if that wakes it.
I've also seen an intermittent tube socket do this, but on that unit, the pins were visibly discolored and didn't grip the pins well either.
I've also seen an intermittent tube socket do this, but on that unit, the pins were visibly discolored and didn't grip the pins well either.