I've used Parallels for many years (started with version 3!) and have only started experiencing problems since I replaced my two iMacs this year. I bought 2 iMacs to replace my late 2009 models. Got high spec models so I could have a Parallels VM (Windows 7) running on each - previous models weren't powerful enough, so used to remote desktop to a Bootcamp installation on a Mac Mini.
The problem is that, usually overnight, but sometimes during the day, the iMacs freeze - always when they aren't being used. The symptoms are black screen (but my energy saving settings switch the screen off after 20 mins), no response from keyboard or mouse, unable to connect remotely either to drives or screen sharing. The machines are still up and consuming power, so have to be hard-reset (holding the power button down), and then started again. I get no reports of a failure when the machines restart.
Just upgraded to Parallels version 10.0.2 in the hope that it was a problem with the software, but issue still occurs. Note that the machines only crash if Parallels is running.
My suspicion is this is something to do with the fusion drive as I never had an issue running Parallels on any other machine. Have submitted this to the Apple support forum too as I haven't been able to find similar experience reported elsewhere. Also used the Parallels "Report a Problem" facility.
Are there any diagnostics can I perform to get a better view of what's happening?