I have been experiencing this, but with Lion, not Mountain Lion. It is driving me nuts!
I am using LG L246WP monitor via HDMI to DVI on MacPro1,1. I have tried changing cables, even tried VGA to DVI (no blackouts with VGA, but not sure I can trust that, because there is no set pattern of when it will blackout!).
I did try another monitor for most of a day - no blackouts/flickers, and as soon as I hooked up my original monitor, I got blackouts, which led me to believe it is the monitor.
I have searched and read several forums on blackouts, each with different configurations, so at this point I am not sure what it is. I even replaced my Graphics/Video card, because someone on Apple forum said most likely that was the culprit, but still having same problem (even as I type this!).
It is like something is intermittently interfering with signal???