Thanks for your post, and sorry you're having a little trouble.
I've not heard of any DEP related issues recently- perhaps a windows update has triggered it?
You should be able to exclude the SQL Backup engine from DEP by right-clicking "My Computer", selecting "Properties", going to the "Advanced" tab, then "Settings" (under Performance). The DEP tab in the screen that appears allows you to exclude the SQL Backup service.
I'm not sure if it will have produced any useful log information if Windows killed the process, although you may find more reasons as to why in the Windows event logs.