"Last backup could not be completed" when "Last backup: Never" I have deleted all major iCloud backups and removed Camera Roll etc. from the impending backup so it should be less than 5 GB. Even still, when I re-enable iCloud Backup and go to sync for the first time, I'm told that the "Last backup could not be completed". Tried power cycling and still no change. What gives?
From the date of your post, you were using iOS 9 at the time. I experienced this issue myself with backups in iOS 9. Forcing another iCloud backup would eventually allow it to complete, but over time I had to deal with runaway backup sizes (growing up to upwards of 5 GiBs after a few days).

As far as I can tell, this appears to be resolved at last in iOS 10. I would recommend performing a backup in iTunes, then upgrading before trying another iCloud backup.