I posted earlier that my 2012 base-model Mac Mini had the black-screen issue. I had to return the Mini due to a different problem, and the new one has the exact same problem with black screens. So, I'm hoping for a software fix. BTW, I looked in the console immediately after a black screen but saw nothing related to a video issue.
This is my second mini that does the same thing as well so I think it's a driver issue. I keep encouraging everyone to call apple support and start a ticket. Mini's are already one of the smallest market areas for Apple so we need to speak loudly about this issue if we want it solved quickly. I can guarantee if it was the iPad Mini doing this it would be fixed in a week with a minor update!