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Mayo, is the 'sleep mode' you refer to in your post different from 'a nap' or what ever it is that my 20" iMac G5, does when I leave it 'unused' over night???
"Sleep" refers to when the Mac's drive "spins down" and the display turns off. The Mac is in low-power mode but it isn't turned off, which is what I presume your Mac is doing if you haven't shut if off before going to bed...
Here is what it says in the SD! user guide:
"If your Macintosh is asleep when the time comes to run the backup,
SuperDuper!’s scheduling won’t wake it up, so the backup won’t run.
The way to handle this is to use the Energy Saver Preference Pane in
System Preferences to schedule a wake (or “start up”) event for a
minute before the backup is scheduled to run."
In the Energy Saver Preference Pane I see options to start-up and shut-down, but nothing that would let me schedule additional "wake from sleep" events... I already use the start-up option every day at 5:55am.