Here is what I decided to try using a sequence of Windows Task Scheduler (WTS) tasks to wake and keep awake the computer thus allowing the RST Utility to do it's scheduled Verify job:
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EDIT - this (below) does not work as Windows7 automatically goes back to sleep 2 minutes after it is woken up unless the waking application explicitly tells it not to. (It ignores the sleep interval timer) So, changing powercfg settings alone will not work. In spite of all those claims on the Internet! (This is to stop the laptop you wrapped in your sweaters in the suitcase from bursting into flames!)
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1) 4.00am. WTS: Wake the computer using a dummy task:
cmd.exe /c "exit"
(just opens and closes a Command Window)
2) 4.05am. WTS: Change Power Options setting to Max Performance = Min energy saving:
POWERCFG -SETACTIVE SCHEME_MIN
(Sets Sleep to "Never")
3) 4.10am. Schedule a Verify at this time using the RST Utility (Notification Area)
4) 5.40am. WTS: Change Power Options setting back to Balanced:
POWERCFG -SETACTIVE SCHEME_BALANCED
(Will allow sleep after 30 mins i.e. at 6.10am)
This scheme allows the RST utility to verify for 2 hours before sleep is resumed - adjust if your verify takes longer/shorter.
It presumes that you are using the default settings in your Power Options and that you normally have "Balanced" set.
(Switching the sleep delay alone seems more complicated!)
I used the "every Tuesday" setting in Windows Task Scheduler and in RST Scheduler
I'll report here if it fails (I can't be bothered to do any test runs) and, of course, I welcome criticism/suggestions.
See EDIT at top of this post