TSM could be the issue if it is running the backup at the same time as your scheduled job as part of a disk backup, although I never found it an issue; as I recall there is an option to backup files without locking; I had a separate TSM task set up eventually to deal with database files.

If there is a separate SQL backup being taken then it could be breaking the LSN chain, although this has only affected Differential backups in my experience.

I think you need to look at the TSM schedules and file options and work around them or change them to times more suited to your SQL backup needs.