I spoke too soon. Having run my test backup/restore, I thought I would now do a full system backup. Configured Veeam to back up the entire computer, except for a specific folder I want excluded, and when I ran the backup the system hung a creating the VSS snapshot again.
No error message. The details panel just listed
Preparing for backup - 28 sec
Creating VSS snapshot - 12min 57 sec
Task Failed Unexpectedly
The task failing is when I reset the system as the PC had become completely unresponsive. No mouse movement, no keyboard response, completely hung.