When it goes bad, go ahead and leave it plugged in for a couple of days to see if this might be a failing capacitor(cans). There were a lot a failing caps around this time. It might be worth it to take a look at the cans on the power supply to see if any are swollen and/or leaking.
I’d also hook up an external monitor when it goes black to see if you can narrow down the issue to a component.