I have experienced this issue on two Mac Minis 2.3 GHz Intel Core i7 (late 2012) connecting to a Samsung monitor using the supplied HDMI to DVI cable and the DVI cable which came with my monitor. This Samsung monitor and DVI cable combination has been used with a previous Windows PC continuously over a number of years without fault.
My first Mac Mini demonstrated two symptoms
1. On random occasions (approximately one time per hour), the screen will go blank for a second, maybe two, and then come back on again.
2. On random occasions (approximately one time per hour), the screen will display a "snow storm" like appearance, similar to an untuned analogue TV screen. To rectify this situation either disconnecting the DVI cable or power cycling the monitor brings the display back.
After logging a call and much discussion and a visit to an Apple Genius bar, this Mac Mini was replaced.
My second Mac Mini has so far only demonstrated symptom 1 once so far, though I'm sure it will continue. I've logged a call again for this new Mac and I've been encouraged to try this mac with a new monitor and cable.
I am now wondering what my best options are, things I am considering are
a) Maybe it is my Samsung Monitor that is the issue? Seems unlikely since my Windows PC works on it. Maybe I need a new/different screen?
b) Maybe I have received my second Mac Mini with faulty hardware? Do I try to exchange onto my third Mac Mini?
c) Maybe there is a software/firmware fix coming? This is a gamble with a deadline. I'm not sure if I can wait given the time deadlines required for exchange or refund?
d) I could try to get a mini display port to DVI connector (that's money from my pocket, and an example of throwing good money after bad) and use that assuming it works -- mixed reports on this -- until apple fixes the HDMI issue? This also rules out the option of me using this Mac Mini occasionally on my TV using HDMI without experiencing the issues.