@olivierlambert The issue turned out to be a problem with the VHD files. The VM is a Windows VM converted from a physical server with disk2vhd. There were 3 disks in total that I had converted.
To resolve the issue, I created a bootable WinPE.vhd (with storage and DISM tools added) as well as another VHD as a temporary holder for .WIM files. I captured the contents of each VHD from the disk2vhd conversion into .WIM files on the temporary VHD. Then I created new .VHD files and applied the .WIM files to the new VHDs.
After this process, the backups are working.
EDIT (Important): I had to re-create the EFI boot partition and use bcdboot.exe to setup the Windows boot. I also made sure that the new .VHDs had the same drive letters assigned as the originals while in WinPE and have the new .VHDs assigned to the VM in the same order that the originals were.