Even though the Exchange Backup DAG component is correctly selected, the backup job option "Information Store --> Backup Method" is set to Full-Database & Logs (Flush committed logs) or Incremental Logs (Flush committed logs) and the job finishes with no errors, Exchange 2010 does not flush the logs.
Exchange is responsible for flushing the transaction logs after a successful Full Backup as specified in the Microsoft documentation:
Exchange "Exchange Full Backups"
Exchange "Differential backups"
Exchange "Incremental backups"
Exchange VSS Writer..Interaction Scheme
In an Exchange 2010 DAG environment there are two writers: "Store Writer" associated to the "Information Store" and the "Replication Writers" associated to the Exchange Replication service when DAG is configured.
The writers can delay the deletion of the logs after a full backup if there are pending operations which affect the logs. For example, if replication among the "Mailbox Exchange servers" is disabled or is not working properly, the logs will not be flushed.
Log truncation doesn't occur on the active mailbox database copy when one or more passive copies are suspended.All the Exchange Database copies should be active and replication should happen for transaction logs to be flushed
Set the Exchange Writers logging level to "Expert" so that Exchange reflects every detail of the Writers operation. See http://technet.microsoft.com/en-us/library/dd233256.aspx for details
a) Check that the Replication is working properly among the Exchange Mailbox servers.
b) To prevent the log drive from filling up with transaction logs, you can remove the affected passive database copy instead of suspending it.