BACKUP failed to complete the command BACKUP DATABASE ... WITH DIFFERENTIAL. Check the backup application log for detailed messages.
I see this message in SQL Server log file viewer. Where is the backup application log?
Finally, I found the problem. It was caused by a Windows Backup on Windows Server 2008, which was also doing a full backup (behind the scene). And this caused that the SQL Server diff backup was unable to find the last full backup.
We solved the problem by migration to Windows Server 2008 R2.