QUOTE
I'm not using any disk! [...] I do have SuperDuper on my desktop as my external hard drive.
I assume you mean you are using SD to make backups on an external drive.
Is that correct?
If so, you are using a "disk." And, for some reason, when you put the Mac to 'sleep', that drive may be turning itself OFF. Can you tell us how it is connected and what brand/model drive it is? And how old? Space available?
It would help if you had some of your hardware and OS information in your profile that is displayed under you name/avatar. Since you haven't added that yet, we also need to ask you what Mac and which version of OS X you are using? Then we'll probably have more specific questions about your setup.
BTW, you can put your info by using the "My Controls->Edit Profile Information->My Macs" section.