I have been having this problem on my Mac Mini Server 2012 (Macmini 6,2) with Mavericks and Yosemite. After much frustration, I finally fixed it.
I have a Dell U3011 (30") monitor connected to the Mini DisplayPort video out using a Mini DisplayPort to DisplayPort cable. The Dell will only display 2560 x 1600 when I use the DisplayPort connection.
I also connected an older 19" LCD monitor to the HDMI video out using Apple's HDMI to DVI connector adapter.
The system worked fine when I first purchased it. After I upgraded the RAM to 16GB, the Dell began experiencing frequent blackouts. I develop software and edit a lot of text. Usually the Dell would black out while I was scrolling through full screen text files, but it would also crash frequently in Chrome.
Sometimes unplugging the Mini DisplayPort connector from the back of the Mac Mini would reset the big monitor, but more than 60% of the time the Dell would not display anything until I rebooted. Shortly after rebooting, the monitor would black out again.
Since the mini shares the working RAM with the video adapter, and the issue started after a 16GB upgrade, I initially suspected faulty DIMMS. I ran the memory diagnostics for 26 hours (start up holding the "D" key while connected to the internet - this is VERY useful) which turned up nothing.
Looking in the console logs there were many warnings and errors related to video output. At this point I started to suspect the operating system itself as the culprit.
I also have several USB to DVI video signal converters. These don't work well for viewing or editing video, but for web software development & testing, as long as you use the software video proper drivers, they work fine. I used to use them with a 2011 MBP that died a premature video card death, but I digress.
After completely disconnecting the HDMI to DVI connector and re-routing the video through the USB to DVI converter, the random crashes stopped completely.
I suspect there is an issue related to memory addressing (64 bit) and sharing the working RAM between the DisplayPort video 'space' and the HDMI video space.
Once I stopped using both video output ports at the same time, all of my monitors worked flawlessly.
Again, once I installed more than 4GB of RAM, this problem started. Once I stopped using two directly connected monitors, it went away.
I didn't try putting back the original 4GB of RAM because the system is too slow and I don't have any more time to spend on this.
Once current projects are complete, I will take the entire system (giant 30" monitors and all) into the Apple Store and show them. I suspect the original fault to be caused by either defective hardware or defective system software. It was not my monitor.
I hope this helps someone - it is a VERY frustrating problem that took several weeks to resolve.