If you are in an Active Directory Environment, QB will default to trying to save the backup as a local computer user. Since I am trying to save the backup on a shared drive, I found that appending the Domain name to the User name allowed the backup to proceed with the correct credentials. 

Editing the backup in Task scheduler allows you to change who the task runs as. In my case it was Administrator, and I changed it to MYDOMAIN\Administrator.

I hope this helps someone.