It seems more than one backup program installed and running. If you have more than one backup program installed on your machine, disable all of the programs except for one and try run the backup job again.

Another possible reason is that previous VSS snapshot has not completed properly and is still running. Try to restart the Volume Shadow Copy service. You can do this by going to Start > Control Panel > Administrative Tools > Services: find Volume Shadow Copy and right click and select Restart.

This error can occur if several backup plans are trying to back up the same data and/or overlap in schedule when VSS is enabled.

Old backup programs are always uninstalled after the first successful backup and restore.

Restarting VSS and running the backup does help, but the error just happens again in a couple days. The backups also complete successfully when run manually with having to do any restarting. It's just when the scheduled backup runs that this error is observed.

Forgot to hit the reply button first^^^^

In that case rescheduling the plans should help. Most likely either another plan or something else in the system is trying to utilize VSS in your system. Another possible reason is that something is wrong with VSS itself so you might want to re-register its core components.