I'm thinking you are asking too much power to the psu it becomes unstable at some point. I'm not really sure a 1000w psu can handle 4 gpus and the rest of the rig, but if it can it would be with some undervolting.
Psu's are not meant to be used at full capacity 24/7, you should either leave some room or modify its cooling. I would bet that your psu is running hot.
7950's are 200W cards, and 1.1kW from the wall = 880W from a 80+ power supply, like that evga. Seems about perfect to me, even within 80% max load like I'd recommend. What is it you were saying again?
Fans revving and randomly going dead while mining sounds like a riser issue to me. When the cards die, is it usually the same card in cgminer? You've shuffled them (the cards) around a bit already, right?
You are assuming the OP uses 120v and not 220v. If he is using 220 he is using almost 1kW from the psu. Also I've read each 7950 draws 225w on stock volts, x4=900w. If he has a cheap 60w cpu and only 2 slots of ram filled he is at 990w. If he is using some good cpu then he is already over the psu maximum capacity. A good psu will shut off if you demand more than it can handle.
1100W from the wall is 1100W, period. All else is irrelevant, no matter what you've "read." Do you even know what we are discussing here?
If he is using 240V, and that's a long shot, the PSU should be more like 85-90% efficient. That would still be 990W at the very most, which I know that power supply is more than capable of doing. If you are so sure he is overloading the power supply, he would see a hell of a lot more than 1100W at the wall. Of course you know power supply efficiency drops a lot when very near the rated capacity, right
I think we are discussing possible reasons of an unstable system. You might be right on the wattage of the cards, but I could still be right about the psu being pushed to its limits.
OP has not stated how much ram and what cpu it has. Their wattage could vary from 75w to 200w easily.
He hasn't as well told us how he measured the the current at the wall. Clamp meters can be innacurate if used incorrectly. He might have used a kill-a-watt though.
220v is not that far-fetched, most of the world has 220v.
And if he managed to position his psu in a way it absorbs some heat from the gpus, the psu might overheat and produce some voltage drops. Since psu its working in between its limits the protection doesn't trigger and the rig remains on.
Other than that the only things that is coming to mind for the rig to become unresponsive would be the ram. A bad ram or insufficient ram making some of the cards produce hardware errors that could make it unresponsive or make cgminer call a gpu sick.
Don't get me wrong, I'm not here to argue with you, but in my experience, when troubleshooting some issue, it is always better to keep an open mind about it
We still need more information to be certain on what the problem is. But I don't think my answer was that crazy though...