Okay, I think I can finally shed some light on this….
I went through all of the suggested fixes for a scheduler problem. I talked to my ISP, and they checked cron and other stuff that I don’t understand and said everything was okay.
Updraft continued to say that my scheduler was broken, and overdue for 13 jobs. To see if it might make a difference, I started disabling plugins one at a time, and as I did so the number of overdue tasks walked down slowly from 13 to 8.
At that point I disabled all of my plugins, but Updraft still showed 6 overdue tasks. When I enabled all of my plugins in one go, however, several of them failed and I was notified that my Genesis version needed to be higher than the one I had in order to use those plugins.
Confused, I checked my Genesis theme settings, and discovered that I had turned off automatic updates off at some earlier point, meaning I was about three months behind the most recent version.
I updated Genesis, enabled all of my plugins, and instead of 13 tasks Updraft now showed only 8 overdue. I decided to wait overnight and see if the overdue tasks would run, and sure enough, this morning not only is Updraft not reporting any overdue tasks, the most recent backup ran without a hitch.
So. To your list of possible scheduler conflicts/problems, I would add: “If you use Genesis on your WordPress install, make sure that you have the most recent version.” [In WP admin, click Genesis / Theme Settings, then looked under Information.]
I don’t understand why the scheudler suddenly stopped working, then worked intermittently, but in any case it all seems to be current/functional now. At least for the past 24 hours.