In Exchange Server 2013, I got one backup issue with Veeam Backup, but the problem occurs with all VSS backup solutions. I was able to reproduce the issue with Windows Server backup role.

In fact, when I checked the mailbox database folder, all transactions logs were not deleted after the backup, even if the backup is reported as successful.

VSS Backup logs not deleted

VSS Backup event

During the troubleshooting phase, in the Event Viewer of the Exchange server, Application folder,  I discovered two specific events in error state:

• VSS event with error code 0x800423f3 :

A VSS Writer has rejected an event with error 0x800423f3, the Writer experienced a transient error.

Event log VSS 0x800423f3

• MSExchangeRepl with error code FFFFFFFD:

The Microsoft Exchange Replication service VSS Writer failed with error FFFFFFFD when processing the backup completion event.

MSExchangeRepl error FFFFFFFD

Mailbox Database

In my case, I found that the Default Mailbox Database was dismounted and not deleted.

Mailbox Database Dismounted

• I mounted the default Mailbox Database and restart a backup from Veeam.

ESE Deleting Log Files

After the backup, no more error but ESE information event to indicate that log files were deleted.

More

You can get more information about VSS Backup here.