I changed the volume of my log files from L to M.
So I changed the information in database properties and moved the log files to the new location using EMC. Since then the backup as completed with warnings. The error says "System cannot find the path specified". I even deleted the backup files on the network share and started fresh but the backup still failed on the same F drive, which is where one of my mailbox databases are located.
But in events manager there is a an event id: 9782 saying that VSS has completed a backup of the database (including the database in the F drive). And the log files for this database will not be truncated.
I did a VMware vmotion just before the first backup started.