iMac Power shutdown

Late 2013 21" iMac. Twice now I have found the computer shut down from sleep mode. No response to power on via power switch. Both occasions removing the power cord and refitting it has worked and the power switch works normally. Very strange. Any ideas/suggestions please. Am I missing something obvious as a Mac newbie?

Normally, I would suggest looking at the power managing settings in System Preferences to see if it is set to shut down after a certain amount of time.
However, the thing about the power cord makes me wonder if either there's something wrong with the outlet or with the power cord itself or possibly the part inside the iMac that the cord plugs into. Can you try plugging it into a different outlet somewhere else in the house and see if the same thing happens again?

If you purchased it new or refurbished, it is still under 12 month warranty Apple Care.

Thanks for your response. I would expect the power switch to operate normally after a power management shutdown. However the power button is completely dead.
I think it's likely to be a hardware failure, but I wanted to check if anyone had a similar problem or if there was something I was overlooking.
This is my first Mac after years of Windows machines with never a failure. I was hoping to keep up my success rate!

It will be under warranty so make an appointment and take it back. Never see the problem you describe and it may be a dodgy lead. Personally use an UPS particularly in a tropical environment with thunderstorms.