Hi,
That still sounds like a broken scheduler. The fact that it runs very occasionally indicates that the scheduler sometimes runs, which can be due to tricks used to kick it into action when you have the UpdraftPlus settings page open.
If you install the WP-Crontrol plugin, and visit Tools -> Crontrol, what do you see? (A screenshot would be handy - use http://snag.gy if it helps).
David