Imac shuts down when it sleeps

I have a new iMac 27" that keeps shutting down when I put it to sleep, & sometimes if it is just left for several hours it'll do it, even though I have it set not to sleep. It then needs to be unplugged for a few seconds, then after about 15-30 seconds it restarts. I just got it in October, it's running Yosemite. It's the 3rd iMac I got from Apple, the first 2, refurbs, did the same thing & I figured I'd gotten 2 lemons that didn't get repaired. Now the 3rd one they sent, a brand new one, does the same thing. Has anyone else had this problem, any ideas what may make the machine shutdown & not respond to the on/off switch?

It's very unusual to get three 27" iMacs that are doing the same thing. Refurbished machines from Apple are like new ones so that shouldn't matter. Where do you live and are you using an UPS (uninterruptible power supply)? Bad or dirty power can cause your iMac to shut down which is why we need to know your location and if you use an UPS.

Dumb question, probably, but do you have the iMac set to shutdown (or start up) at certain times in the Energy Saver settings? Or any maintenance programs set to run periodically?

In Doylestown PA, not using a UPS, have a HDD attached for Time Machine, & another for iTunes.
The thing is, it doesn't just shut down, to be started up again by pressing the on/off switch, it won't respond to the on/off switch & needs to be unplugged for a while, at least 15-20 seconds, sometimes longer, then when plugged back in it still doesn't respond to the switch, but after 30-40 seconds restarts.

It's almost impossible to have this exact same problem happen on three different computers…AND it be a problem that almost no one experiences (very rare).

This has almost 100% got to be a setting of some sort…or a condition external to the computer. For example…frequent power outages (short or long power outages). Especially with a desktop computer without a UPS. If it were a laptop/notebook computer (that has a battery)…this wouldn't happen.

- Nick