Maybe replace the cable? I had a monitor that did the same thing over DVI, blanking out every few minutes. Replaced the cheap pack-in DVI cable with a better one and then it was fine.
That was my first thought as well. I tried a $100 Blue Jeans HDMI cable we had here at the office but there was no change.
It's interesting to me that the blanking events are grouped together and mostly in the beginning. My best guess is that the monitor adjusts some timings and eventually gets it right, and whenever it's turned off it has to figure out the timings all over again. But I don't really know what I'm talking about...
