Please check/try the following:
1) in the exchange server check the vss writers:from the CMD type vssadmin list writers and check if the Exchange writer is "ready" or ina "retriable" state..in the last case do a reboot of Your exchange server.
2) did you manually deleted the log files on exchange or the full backup missed to delete some log files, if so, clean the log files with the exception of today and the day before than run a full backup.
3) delete all the exchange job backup and recreate them completly before test the job again.
let me know if it works.