Have to say it sounds like psu to me, I had same thing happen with a PC some years ago, fresh install, all good for a few days then it would switch off at random. have to confess I kinda blamed the user for it with all the stuff she had on it. then sitting there while seeing what it could be it happened to me. random shut off and restart. after taking it all apart checking to see if M/B was shorting out ect. and trying different ram, even CPU it still did it. I assumed it couldn't be PSU as that was new, but after swapping out for another it cured the problem. never did it again, RMA time for that PSU and all the time spent trying to sort it you never get back of course.
The thing with an issue like this, it can take a while to track down.