Have you checked the Backup Report for the job in the SMSQL Management Console? In the left pane drill down to Reports => Backup => <Timestamp of Backup Job> and it'll give you step by step details of the backup job so you can see at which point it failed.
It may also be worth checking the MS Event Logs at around the time the backup job failed to see if anything shows up there.
I had same problem Backup failed error code 0xc00408d3 but I found that my database had a SQL database snapshot and I delete the SQL database snapshot and run again the backup now it work fine. Verify if you database have a SQL database snapshot delete it and run you backup using Snapmanager.