If your Hyper-V VM is unresponsive during the 'Taking Shadow Copy' phase, then it's likely that the VM is going into a Saved State for a minute or two, due to the fact that it doesn't meet Microsoft's live backup requirements.
In order to confirm if this is the case, run these two commands from command prompt on the Hyper-V Host:
diskshadow /l c:\diskshadow.txt list writers
After it finishes populating the information, browse to the root of the C: drive and open the txt file. What you're looking for in this case is the "Microsoft Hyper-V VSS Writer". Under this writer, each 'Component' will show the VM's name and whether it is backed up in:
- a Saved State (Backup Using Saved State) or;
- a Live State (Backup Using Child Partition)
In 2012R2, the terminology has changed and you'll see Online (Live) or Offline (Saved). The reason for this mainly is that 2012R2 Hyper-V does not interrupt the running VM's, which was made possible by taking a checkpoint and then merging it back in. If you'd like to read further on this, you can read this blog post by Ben Armstrong.
Thereby if you see the VM marked as Offline on your 2012R2 host, it won't be interrupted during the shadow copy, but VSS won't be running inside the VM, so you might still want to look into why that is by going through the requirements.
Windows Server 2016 hosts and newer are not affected by this as we are not running VSS through the host and are using production checkpoints through their API as specified by Microsoft.
An example of what you'll see in the text file: