Since you said backup software I'm assuming you're using a third party solution for your SQL Server backups. We've had problems in the past with backup software and it can sometimes cause problems/contention with SQL Server native backups by creating a blocking situation.
What I've done in the past has been to stop the backup software (in our case it runs as a service on the server), then stop and restart the SQL Server Agent. Finally, remember to restart your backup agent service. This solves the problem 99% of the time and doesn't require a restart of the server.
Hope this helps with your problem.
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