I am using Windows Server 2008 R2. I was also trying to use Windows Server Backup to mount a recently backed-up vhd. My Windows Server Backup program was also stuck forever at "Reading Data Please Wait." (My vhd was saved to a USB-mounted external drive).
I am not going to answer the question of "What is the underlying problem here?" Because to me the more important questions is, "Is there another (easy) way to achieve my goal? There sure is, and it's built into Windows.
Here's how I achieved my goal.
First, you have to kill off this stuck backup process. Super simple: Just go into SERVICES and restart "Block Level Backup Engine."
Now that we are out of that stuck program, we still need to get into the Windows Server Backup vhd.
I was able to very quickly and easily mount the backup vhd as logical (usable) hard drive by using a built-in Windows program called DISKPART.
Follow These Easy steps:
Open command prompt and just type DISKPART
It returns a few lines indicating that DiskPart is started.
Next type SEL VDISK file=”the-location-of-your-file-including-the-file-name”
For example:
DISKPART> SEL VDISK file="J:\WindowsImageBackup\99-DC02\Backup 2017-01-16 070031\2a7efb56-0b8e-11e4-8d4c-806e6f6e6963.vhd"
It returns: DiskPart successfully selected the virtual disk file.
Now type ATTACH VDISK
It returns: 100 percent completed
After a few secs, your vhd will mount as a new logical drive. You can now dig into this drive with your Windows Explorer GUI just the same as any. I was able to retrieve files that I needed by dragging them to the desktop.
When you are done retrieving files, and you want to quit, go back to your command prompt window and type DETACH VDISK
It returns: DiskPart successfully detached the virtual disk file.
Thank you Microsoft for an Excellent Utility!