Task Scheduler wakes up, but goes back to sleep

I am running Vista x64 (Ultimate) and am using Acronis TrueImage for backups.
Acronis has a built-in task scheduler, but unfortunately it doesn't provide
an option to wake up from sleep. I had contacted their tech support about it
and they showed me how I could run the task from the Windows Task Scheduler,
which was great. However, a strange thing happens. If the computer has to
wake up from sleep to run the backup, it seems to wake up, and then
immediately go back to sleep. When I turn on (wake up) the PC the next
morning, I find that Acronis TrueImage has just started to run. It leads me
to believe that the "C:\Program Files (x86)\Common
Files\Acronis\TrueImage\TrueImageService.exe" that gets run spawns a new
process and then exits. If that's the case, is there any way to make the Task
Scheduler wait for spawned processes to finish executing?