I think I’ve found the problem here. It seems to have been a conflict between two backup programs.
In addition to UrBackup, I had been running Carbonite on the client computer. Carbonite was for off-site backups, UrBackup for local backups.
According to the Carbonite docs, it uses VSS, as does UrBackup of course. After I stopped the Carbonite backups, UrBackup has run properly for several days now.
I can only assume that the two programs were interfering with each other, perhaps in their use of VSS. I’m going to re-enable Carbonite now, but will set up backup windows so that the two programs aren’t ever running at the same time.