Why does my iMac 27" (late Dec 2012) keep shutting down unexpectedly?

Same problem here. iMac 27 late 2013.

But it also crashes on iMovie sometimes. I suspect that FCP and iMovie tax the memory and maybe access some areas that other programs do not.

The thing that I cannot power it up immediately is strange, though. If it is some RAM module in bad shape, this shouldn't be expected. But maybe it is just some form of auto protection of the machine itself... Go figure. Maybe it is just temperature?

How hot is your environment?

I have had similar problems with my late 2012 iMac 27. Random shutdowns. Like someone pulled the power cord. Would not power back on until I disconnected the power cord, wait a minute or so, then reconnect cord and press power button. A couple of calls to Apple Support... eventually wiped HD, assuming it was a software problem. Reinstalled OS X and shutdowns continued. Brought iMac to Apple store. Hardware tested fine. Tech felt that it was still software. Tech did a format and repartition of HD. Brought iMac home, and within an hour random shutdowns continued. Brought iMac back to Apple again. They replaced the Logic Board and Power supply. I've had my iMac back home for a couple of weeks and so far, it's working perfectly. Fortunately, my Apple Care was still in effect, as the repair would have cost $900.

iMac 27" late 2012 unexpected shut down multiple times in a day:

Apple store Fountain Gate replaced the Hard drive on my first visit 28th Nov 2015. The problem still persist. On 10th Dec 2015, my 2nd visit to Apple store Genius bar they replaced the logic board & power supply. This is few months before my Apple Care expires which is Feb 2016. I'm all smile knowing the problem will go away BUT IT DIDN'T. My most dreaded fear. The random shut down didn't happen after the 3rd month post repair, March 2016. From December to February I hardly use my computer. I only use my iMac mainly for browsing & youtube that time. No heavy app. My guess is the 27" iMac late 2012 is generally a bad apple.

So replacing the logic board & power supply didn't fixed the annoying problem on my iMac. It means I paid for Apple Care for NOTHING. I am now out of warranty with this lemon. The title of "Proud Owner of the most advanced software/hardware, most elegant design desktop computer" was cut short by the iUSDS aka "iMac unexpected shut down syndrome"

(and they also changed the display panel, LCD because they accidentally brake it...and that delayed the return of my iMac for another week). The genius lady wasn't very happy when i picked up the iMac from repair. Did she broke it? I don't know. GENUIS!

the key board that comes with my 27"iMac late 2012 is acting weird upon log in. This is when the iMac first start from power on. It enters multiple character everytime i pressed one single key. The battery still 90% & I'm using energiser battery as the genius bar recommend. I have to remove the battery & put it back again to make it work. That somehow fix the problem. I wonder if theres a connection with the iMac unexpected shut down?

note: Genius Bar thinks theres nothing wrong with my apple wireless keyboard😕

Helpful tips is greatly appreciated, Thanks heaps😎