This problem can be caused by one or more malformed registry entries in the HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Enum\{CB107E6E-5323-489e-AD3C-907943A99D83}\VDisk subtree.
If you have experience safely using regedit, you might be able to solve the problem by using it to delete the entire VDisk subtree, above. WARNING: Stop and ask an expert's advice if any of these instructions are the least bit unclear. You can easily make your computer unbootable by improperly using regedit.
First dismount your virtual disk(s) as usual. Then right-click the VDisk key and select "permissions". Click "add", enter your username, and click "OK". Then, with your username selected in the upper pane, check the box "full control" under the "allow" column in the lower pane and dismiss the dialog by clicking "OK". Finally, right-click the VDisk key again, select "delete", and click "yes" in the "confirm key delete" dialog box.
Now try mounting your virtual disk(s) again.
For some older versions of VHDMount, this problem can also be caused by the issue described here.