Step 1: First you should verify the backup type ,whether it is Full or Incremental backup because Full and Incremental backups will truncate the transaction log files, whereas Differential and Copy will not
Step 2: it may be problem with “Microsoft Search Indexer Service” that means not allowing the replication service to truncate logs, so you can stop the IS service and delete the copies of catalog files in mailbox database location. then you can start the service, and try backup now.
Step 3: you can verify event log for any transaction log sequence issue.if it is found you can dismount the the mailbox database then find state of the mailbox database, you can use the following command: eseutil /mh “edb path”, if you getting clean shutdown. you can delete the logs.
Note: Before to delete logs. you can move the logs to other drive and delete in source location
Please note: if you are using site to site DAG, you would need to increase the band width because it may be issue is related to copy queue length but we increase the copy queue length would be Zero, log file will be truncated automatically if any bandwidth shortage, it will not truncate the transaction logs