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

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?