Why would a user who is a member of the 'backup operator' group be unable to run a task? It simply does not start - there is no error that I can find. I changed the user of the Windows Server Backup from admin to svc_backup to avoid changing the password periodically in two places (svc_backup has a non expiring passsword) but the svc_backup user cannot start the backup task.
What can I check?
Check that the Backup Operators group has been granted the "Logon as a batch job" windows right. This is the default, but may have been changed.
Also, try to right-click on the task and select Run to determine if it launches in that scenario.
I would also select "Run with highest privileges" and "Run whether the user is logged on or not".