"Microsoft Software Shadow Copy Provider" goes into a hung state i.e. "Stopping".

I've solved this issue by deleting, then recreating the service.

These are the specific steps:

If the service is in the "stopping" state, kill the PID
   tasklist /svc | findstr swprv
   (it will respond with svchost.exe  #### swprv)
   issue the command    KILL  ####
   where #### is the number of the PID found above.
Check that the "Microsoft Software Shadow Copy Provider" service has stopped.

Now we will remove the service with the following command:

   sc delete swprv

Refresh the Services view and the "Microsoft Software Shadwo Copy Provider" should be gone.
 

Now we recreate the service as follows:

   regsvr32 /i swprv.dll

Check that the service has been recreated.

Test a systemstate backup.
The service should start & stop as designed.