Why does the external monitor on my MBPR constantly lose its signal?

I have a Macbook Pro Retina, manufactured in August of 2012 (mid 2012). The laptop seems to be incapable of continuously driving an external display. On some monitors it will lose the signal once or twice a day; on my home monitor it will lose the signal many times an hour, sometimes taking minutes to "settle down". The effect is as if I had un-plugged and re-plugged in the HDMI cable. However I see this happen on three different monitors, two of which come in through HDMI and one through Thunderbolt. I even bought an apple monitor for $1000 that I returned, because on that one every now and then the MBPR just wouldn't detect it at all (and I would still see it quickly drop and re-establish the signal a few times an hour).

Here is a video of what that looks like, as it flashes to blue repeatedly: https://dl.dropboxusercontent.com/u/19671563/IMG_1363.MOV

I tried gfxCardStatus and using Discreet Only, no luck.

The apple store guys were no help. They claim they have never heard of this issue even though I repro it *daily*. When I check the Console, this is the first message I always see during an incident (for the worst-performing monitor, at least):

8/24/13 4:30:01.312 PM WindowServer[82]: Received display connect changed for display 0x3f003d

I have tried every conceivable Display setting (Best for Retina display, Best for External display), and I am mirroring. I never had even a single problem on my older Macbook Pro; I have had problems since day 1 on my MBPR and they are getting worse (i.e., the external monitor is losing its signal more frequently every day).

Can anyone recommend a solution or suggest a cause?

Thanks,

-Eric