As those above have expressed... I have a 2011 27" iMac which has the same intermittent black out problem. I've taken it twice to the genius bar for complete tests over a couple of days.... you know, those diagnostics that we don't have access to. They found nothing... I'm at my wits in.
Here's the problem though with the replacement video card program problem..... Apple won't replace the video card unless they can see it has a problem. This is what they told me at my local Apple store. So... until I can show them the problem, they won't replace the video card.
However.... I'm starting to have my doubts that it's a hardware issue. I'm curious if somehow Adobe flash isn't doing something. Maybe it's a Mavericks bug... I just don't know. I have tried everything except reinstalling OSX. If that is the solution... then it's a software problem and Apple should be aware of it and fix it with an update.
I really need to upgrade my iMac, but I just can't buy another iMac if there is an inherent design flaw. The Mac Pro is just impractical for me... and the Mac mini is a 3 year old design... doesn't even have USB3!.
Obviously.... not a happy Apple customer at the moment.