Same problem here - Cables etc. are fine
Same problem, same hardware. Sometimes the screen goes blank once every 30 secs, sometimes once every 3 minutes, and sometimes it just goes "jumbled jigsaw" on me, with sections of the screen content appearing randomly tiled like those little slider-jigsaw puzzles from the 80's.
This is not an uncommon issue - in fact, I believe that almost all people with the setup [Mac Mini 2011] + [24" Cinema Display] are experiencing similar problems. I suspect that it may have something to do with integrated GPU providing a refresh rate of 59.7Hz to a 60Hz display (or 49.8Hz to a 50Hz panel). The "blank screen moments" are caused by the GPU and display re-synchronizing the signal, hence the semi-random cyclical nature of the problem. That's just my opinion, baseless as it is.
No matter what's wrong and where, though, this simple problem needs to be fixed. Apple itself is the manufacturer of these goods (in a very roundabout way) so there is no excuse for what appears to be a third-party compatibility issue.
This is certainly a problem I did not expect to encounter having migrated away from PCs (er, I mean, Windows) for that very reason: 1001 cooks, working in 1001 kitchens, on just one broth.