on a side note I had the same kind of screen blanking issue with my xbox 360 connected via HDMI to my TV and it turned out to be the cable, I tried a couple of other HDMI cables and it didnt happen again.
I agree with you 110%. Black screen/flickering is actually a very common problem with HDMI. So common that I do NOT believe that this is even a Mac mini issue. This would also explain why it's not effecting the Thunderbolt port. These same symptoms effect every brand of electronics, and usually it can be traced to cheap cables (people believe that because it's not analog that cheap cables work the same as good cables, which is a misconception) or a bad setting (like refresh rate, resolution, etc). If I was troubleshooting this issue I would first start with trying different screen settings, like refresh rate, display profile, screen resolution and 1080i VS. 1080p. I would also be looking at the monitor’s menu. One of those combinations should fix it (providing the cables are not cheap)