I just returned an Apple TV to the nearest store. After three days of troubleshooting, I figured out that the problem was a bad video card. It worked for less than a week, and I was constantly having problems that I couldn't nail down.
Rebooting sometimes worked; restoring video for a few minutes. Eventually I connected the Apple TV's component outputs directly to my tv (Sony Bravia KDL-52V5100), and that worked for about ten minutes; then it too started blinking on and off. The picture was visible, then not visible, then visible, then not visible...
While the component cables were directly connected to the tv I still had the HDMI cable connected through my receiver (Onkyo TX-SR507), and the loss of signal showed there as well. The Apple TV video output was failing.
I checked the HDMI cables by using them with my Blu-Ray player (Samsung BD-P3600). The cables (which I paid $0.22 for!) were not the problem. The signal from Blu-Ray player routed through the receiver to the tv with no problems. You can easily eliminate the cables as the issue by using them with a second HDMI device, taking the Apple TV out of the loop.
In the end; after consulting with Apple Support (Apple TV was less than 2 weeks old), we came to the conclusion that it was likely a bad video card. They set up an appointment at my nearest Apple Store, and I was able to get a replacement immediately, as their brief test showed, the video output was not functioning properly.
I got a new Apple TV and all is good. Solid signal, and no problems noted since yesterday (15 July) at 10pm.