Then that's not good, and sounds like you've got a bad MLB. Not sure why they would have replaced the PSU if the symptoms were the same last time, but Apple is a very strange company, and hasn't had any more success in weeding out the morons who don't know what they're doing than any other retailer with a service department.
If I were to venture a guess, I'd say the SMC chip is bad, and keeps getting a corrupted state. When you unplug it for a time, the capacitors maintaining that state will drain and it resets when they deplete. The fact that it keeps getting corrupted means that there is something very wrong.
So unless you'd like to add to the story that you have a program like smcFanControl installed, or anything that might alter the fan speeds on the iMac, or just interact with the low level system functions... You're likely looking at a new MLB, so I hope you have some kind of warranty on the unit still. If you have some program like smcFanControl, then I would start by getting rid of that and hoping the damage it did isn't permanent.