I figured out what the problem was for me. I had transferred the WP site to a new host. Was testing BackWPup before making change in the DNS for the domain to the new host and it wouldn't run - no logs or errors.
I went ahead and changed the domain DNS to reflect the IP of the new host and see if that backup would then work. It did. I can only conclude that BackWPup requires that the DNS of the website its running on is correct.