Logs are not truncated on Microsoft SQL server after a successful backup.
The following error can be found in the Windows Application log or in VeeamGuestHelper.log file (in earlier versions this log file is called VeeamVSSSupport.log) located in C:\ProgramData\Veeam\Backup on the guest:
The server principal "NT AUTHORITY\SYSTEM" is not able to access the database "Database name" under the current security context.'
or
The server principal "domain\username" is not able to access the database "Database name" under the current security context.'