I could not get the plugin to transfer the files via FTP or DropBox (only tried those two methods). After pulling my hair out trying to figure out why, I now know what was preventing it.
The web hosting company uses the "Hepsia Control Panel" which has a "feature" that automatically determines which outgoing connections to block. For some reason it blocks BackpWPup. You can either disable the feature or add your site's IP address to the list of allowable IPs, and files can be transferred.
- Site console
- Outgoing Connections