Backing up the D: drive simply attempts to back up all the files on the D: drive.
The Hyper-V specific methods of backing up VMs use the Volume Shadowcopy Service and VSS requestors and writers to allow the guest OS to intelligently participate in its own backup process. The success of this method is highly contingent upon the Integration Services/tools being properly installed and enabled on the guest OS.
If you do not backup the VMs through Hyper-V, another way to get good backups of your VMs is to simply set up Windows Server Backup on each one of your guest VMs themselves.
You will not get good backups of your VMs if you simply copy the VHD[X] files while the VM is running, because the VMs are in a volatile state, with data in RAM, etc.
As for why the backup is failing when set to a certain configuration, we would need all the relevant events and errors.
Backing Up Virtual Machines
Hyper-V uses one of two mechanisms to back up each VM. The default
backup mechanism is called the "Saved State" method, where the VM is
put into a saved state during the processing of the PrepareForSnapshot
event, snapshots are taken of the appropriate volumes, and the VM is
returned to the previous state during the processing of the
The other backup mechanism is called the "Child VM Snapshot" method,
which uses VSS inside the child VM to participate in the backup. For
the "Child VM Snapshot" method to be supported, all of the following
conditions must be met:
Backup (volume snapshot) Integration Service is installed and running in the child VM. The service name is "Hyper-V Volume Shadow
Windows 2000: Backup Integration Service is not supported.
The child VM must be in the running state.
The Snapshot File Location for the VM is set to be the same volume in the host operating system as the VHD files for the VM.
All volumes in the child VM are basic disks and there are no dynamic disks.
All disks in the child VM must use a file system that supports snapshots (for example, NTFS).
In general, the process for backing up VMs is the same as described in
Overview of Processing a Backup Under VSS. The unique behavior happens
when the Hyper-V VSS writer (part of the "Hyper-V Virtual Machine
Management" service) processes the PrepareForSnapshot event. If the
backup was done using the "Child VM Snapshot" method, there is
additional processing done but it is not visible to the child VM.