Exchange logs not being truncated

Make sure truncation is enabled within Backup Job

VMs processed by Veeam Backup & Replication must have Application-Aware Processing enabled to perform truncation.

Confirm this by editing the job, going to the Guest Processing tab, and ensuring the Enable application-aware processing is checked. 

In addition to making sure Application-Aware Processing is enabled, check that truncation is enabled at the granular per VM level. Click the [ Applications... ], then in the window that opens, highlight the Exchange server and select [ Edit ]. Within the processing setting window, make sure that the job is set to either "Require successful processing (recommended)" or "Try application processing, but ignore failures," then make certain "Process transaction logs with this job (recommended)" is selected.

Make sure the job is Notifying the Exchange VSS Writer

On the Exchange server that was backed up, navigate to C:\ProgramData\Veeam\Backup and open the most recent VeeamGuestHelper log file.

Within the VeeamGuestHelper log file, search for: "Notifying writers about the 'BACKUP FINISH' event."

After that line will be a list of each VSS writer notified of the 'BACKUP FINISH' event. When the Exchange VSS writer is notified that it has been backed up, it handles the truncation process. There may be multiple lines regarding the Microsoft Exchange VSS Writer, the most important of which is the one that will end in "Ok." which signifies that notification was successful. 

Example:

Notifying writers about the 'BACKUP FINISH' event.
  Truncate logs: [true].
    Notifying a VSS writer about the successfully backed up components. Writer name: [Microsoft Exchange Writer]. Class ID: [{guid}]. Instance ID: [{guid}].
      Writer was notified about the successfully backed up component. Component's logical path: [Microsoft Exchange Server\Microsoft Information Store\EXCH-MBX]. Component name: [guid].
      Writer was notified about the successfully backed up component. Component's logical path: [Microsoft Exchange Server\Microsoft Information Store\EXCH-MBX]. Component name: [guid].
    Notifying a VSS writer about the successfully backed up components. Writer name: [Microsoft Exchange Writer]. Class ID: [{guid}]. Instance ID: [{guid}].. Ok.

Entries about other writers were removed from this example for conciseness.

• If the Microsoft Exchange VSS Writer is being notified of the BACKUP FINISH event, the investigation should shift to reviewing the Windows Events for entries from the Exchange application regarding truncation and backup events.
• If the Exchange VSS writer is missing from the log or failed during the VSS operations, investigate the VSS writer's current state. Run the following in an Administrative Command Prompt on the Exchange server:

  vssadmin list writers
  

  If the writer is not listed or is in a failed state, the Exchange server should be rebooted, then it should be verified that the writer returns and shows as Stable/No Error. Once this has been done, retry the Veeam job and verify log truncation.