Database Full Backup fails being deadlock victim
SQL Server backup operations do not acquire locks, see - Paul Randal's post.
Therefore BACKUP DATABASE... or BACKUP LOG... cannot become deadlock victims. 

Probably some other queries that take part in your backup jobs take part in deadlocks.

If you can describe your backup solution in detail, we might be able to help you.

I personally recommend Ola Hallengren's backup solution to do the job.