When installing windows on a new drive make sure the backup drive (if there is one) is not plugged in during install.
It might mark it as System which would keep you from being able to use it as a backup/restore drive.
This happened to me after the main drive on a Windows Vista system failed.
I had the backup drive plugged in while installing a new version of windows on a new drive (which is always a risk anyway).
Somewhere along the line the backup partition was marked as System.
What I had to do is create a new partition on the backup drive after shrinking the current one. Then I copied all of the backup files (along with the MediaID file).
Make sure you can see Hidden/System files when doing stuff like this.
Then, and only then, did it start showing up in the Restore files dialog.