Since I developed the first version of my script automssqlbackup, I kept getting a ‘Backup failed for Server’ exception on one specific database. All other databases created their backups without error. The only visible difference between the failing database and all other is its size: some 40 GB which generate a differential backup of about 500MB per day.
Some research brought, among numerous questions in forums, this MS KB entry: FIX: You receive an error message when you try to create a differential database backup in SQL Server 2005. It provides a hotfix and indicates that the problem might be fixed in a post-SP1 service pack.
I applied SP3 to SQL Server 2005, and the script can now backup all databases on the server successfully.