I found a workaround that got my scheduled backups working again. It has a number of steps, but it's not as difficult as it may seem, if you follow my steps carefully--it can be completed in five minutes. It is certainly worth the trouble to get this otherwise great plugin working as expected:
* I installed and activated the WP Crontrol plugin: http://wordpress.org/plugins/wp-crontrol/. This plugin gives fine-grained control of WP Cron events.
* This next step is not really an action; however, it is necessary to verify that the problem that this workaround addresses is your actual problem: I went to Dashboard | Tools | Crontrol. This page lists all active WP Cron events in the system. There was nothing there related to Online Backup for WordPress, even though I had a schedule supposedly in place--this is the problem in this support thread.
* Next, I went to Dashboard | Online Backup, and then clicked the Schedule tab. I clicked the "Apply Schedule" button. Since I already had a schedule programmed, what this step did was simply to save the schedule again. If you have no active schedule programmed, then you should configure your desired settings before clicking "Apply Schedule".
* I went back to Dashboard | Tools | Crontrol. This time, a new event had been added somewhere in the middle, with Hook Name "wponlinebackup_start". However, the Recurrence for this event was listed as "Non-repeating". This seems to be a key part of the problem. I don't know why it isn't set with a recurrence value. Anyway, the workaround in the next step fixed the problem.
* For the "wponlinebackup_start" line, I clicked the "Edit" option. This brought the "wponlinebackup_start" event in WP Crontrol to the bottom of the page. I left all the options intact except that I changed the "Event schedule" to "Once Daily (1 day)". You should set this value to whatever recurrence schedule you want (presumably the same thing you had set earlier in the Online Backup Schedule tab). Then, I clicked "Modify Cron Event »".
That's it! The "wponlinebackup_start" was then listed with a "1 day" recurrence, and it has worked ever since--the backups have since run regularly on schedule. I applied this workaround on two different sites with the same problem (and with different plugin combinations), and it worked for both to enable daily backups. I hope that the plugin authors fix the problem (hopefully this WP Crontrol analysis might even help them find the root of the problem in their code), but until then, I hope this workaround helps other people with the same problem.
freedom1 and kimbacaffeinate, could you please post to say if this works for you?