sleep option after a scheduled backup not working

[dnanian]

You mean authorize? It wouldn't authorize again, since it was already unlocked.

Your files aren't secure either on the source or the backup; you can just turn "ownership" off and get access to anything on the external drive. And, of course, when you start up from the backup, you get access to your files when you log into your account.

You can create an encrypted sparse image with Disk Utility, though. Note, though, that you cannot boot from the backup if it's in an image until restored.

Is your Home folder FileVaulted?