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I understand this has no bearing, but having no issues under ESXi 5.1 using Windows Server Backup. I assume you've checked the logs? Possible VSS issue?
What version of Hyper-V (Windows Server)? Are there any errors on the Hyper-V host's event logs after the guest goes offline?
We had a similar problem with Hyper-V guests and Windows Backup under certain circumstances, on Windows Server 2012. The issue was related to heavy guest virtual-disk utilization, which is pretty typical during backup. There were errors in the host's event logs which made the problem pretty apparent (and locatable via Google). Microsoft issued a hotfix, around July IIRC, which has solved our problem.
I'd give you more details, but I don't have the notes from the issue handy at the moment. But double check the host's event logs....