I have a late 2012 27" iMac, running OSX 10.14.4.

A few weeks ago it started randomly shutting off. Not like a shutdown or restart process. More like a power failure. Instant off. It only did it a few times over a few days and then stopped doing it for many weeks. I thought it was gone. 

Now it's back and it's back with a vengeance. Today it's powered off about 10 times! Sometimes it powers off during startup directly after the last power down (when switching from white startup screen to the account selection/login screen). Other times it powers off at seemingly random times during work - there isn't a specific action that triggers it.

Once it loses power, the only way to get it started again it to unplug the power cord for a while, and then plug it back in and turn on.

Is my power supply dying? How can I tell what's at fault?

Clearly with a machine this old I'm due for an upgrade soon anyway. So I don't want to invest in an expensive repair. But if it was an easy fix, that would be worth it. Otherwise, it looks like I might need to order a new one ASAP as I can't get any work done like this.

Any advice much appreciated.