Purchased 4GB Mac Mini, Jan 2012- Had initial problem with Thunderbolt display right out of the box- the fan was broken and sounded like a jackhammer. Sent it back to Amazon, got a brand-new one, **Just did it! While I was typing, the screen went black!** and initially it worked fine, then a few minutes later had a random black-out of the screen. Could still hear sound through thte screen speakers- This now occurs randomly about every 10-45 minutes. To make the screen come on, I have to reach behind the Mac Mini, unplug the Thunderbolt display, and wait a few seconds, then plug it back in. It resumes working, whatever I was viewing has continued (like this forum). I have updated the Mac software, and the display states it does not need any updates, and will not allow the Thunderbolt update to install.
In the course of troubleshooting this with the Apple Care specialist, she had me do several hard shutdowns, to save time, and the Mac Mini developed a disk error that required me to do a full reinstall, and lose all of the stuff I had just transferred from my other desktop. Luckily I only had a couple of weeks of un-backed up stuff to lose. The disk error occurred again, and this time I simply exchanged the Mac Mini at Best Buy (it was within 30 days). I set up the system, checked for updates, and with the new Mac Mini machine, I am still having these intermittent blackouts. I ran a troubleshooting analysis program last week, and sent it to Apple, and the results are pending.
If you are having similar problems, please document them, because the Apple care specialist seemed to have never heard of this problem.