I took mine in four times. Video never failed on the test bench, nor did it ever fail any of the diagnostic tests. The local Apple Store elected to replace the video card at no charge - and I suspect they ate the cost because they said they could not qualify for a free replacement in the program without a test failure. (Apple telephone support interceded at one point and may have sent the video card - I've had so many conversations with everyone that I am not clear on what went down.)
Video had been failing at home within a few hours of "getting it back" (video often would not work for hours after being shut down following a failure). It's been running for a few days with the new card without any issues, although in the early days of failure it would go more than a week before the video would fritz. So the jury' still out. I was sympathetic to Apple refusing to replace it without a diagnostic failure, as I am sure it could be many other things besides the video card.
A weird side effect of the new video card: For the first time, my iMac gets decent internet bandwidth. All my other devices routinely got 25 megabits plus on my connection, but my iMac could never get more than 5 or 6 (it would start out strong and then rapidly degrade when checking it on speedtest.net). Now I am at 30 megabits plus. All the wireless devices are in the exact same spots. Does this make sense? I believe the speediest.net app is Flash - might that have been choking because of video processing issues and throttling effective bandwidth?