I found the other week that my Hyper-V server, running Server Core and nothing else was restarting all of its own accord. As this is just a server at home, and the monitor is switched off 99% of the time I had not noticed it blue screening.
So looking in the event log (remotely of course, as it was running Server Core) to see why, I noticed it had done the same thing every day at a few minutes past 1pm – one of my scheduled backup times during the day.
I was getting Event ID 1001 at about 1:03pm each day. So I changed the time of the backup (using Windows Server Backup, command line) to 11pm and I got 1001 bugchecks at 11:03pm each day.
There was nothing else recorded in the event log, apart from the usual system start/TCP-IP etc messages and no clue as to the reason for the failure. All I had was the BugCheck, an example being 0x0000007e (0xffffffffc0000047, 0xfffff80003676b48, 0xfffffa60019ff5c0, 0xfffffa60019ff660.
A bit of research later, and ignoring most of the posts regards VSS and Hyper-V I came across http://support.microsoft.com/kb/958662/en-us and http://support.microsoft.com/kb/960038/en-us (the latter of these is a hotfix) which I applied and solved the problem.
It would seem that Hyper-V and VSS based backups have an issue with some backups if a virtual machine is in a running state. It is possible to save the Hyper-V guest machine and then back it up without issue, but of course this kicks people of the virtual machine – a bit pointless really unless its a development machine. To turn off backup for a Hyper-V machine, so that the server does not bluescreen then either disable the Backup (volume snapshot) option in the guest machine settings, under Integration Services or install the hotfix and reboot once.