Vss errors during any backup are usually related to a VSS writer that is in an error state.
This can be found by performing vssadmin list writers from a command prompt (more details in one of the other solutions)
With VSS errors on Hyper V backups this can be down to one of the Virtual machines selected for backup
Typically you may receive an error like
VSS Error: Couldn't take snapshot (IVssBackupComponents::GetWriterStatus(Microsoft Hyper-V VSS Writer): 0x800423f0: The shadow-copy set only contains only a subset of the volumes needed to correctly backup the selected components of the writer.)
the 1st step would be to rule out any VSS issues with the host by performing the list writers command, if everything is stable and its just the Hyper V VSS that's in an error state then performing a system update / reboot usually clears the problem.
If the above does not solve the issue then try changing the backup selection to just one virtual machine and then repeating the backup, you may find a single machine is the cause and all the other selected machines will backup fine, keep repeating this process until you have identified which machines will backup and which ones will not.
You may find the backup option is not enabled on the virtual machine that could be causing the problem or it has been seem in the past where this option needs to be disabled and the backup will work. this setting can be found in the hyper v manager.