You may want to contact support for help with this if you are unable to backup automatically and you've confirmed that permissions are set correctly. As far as I know, the automatic backup should happen without prompting under a limited user as long as the destination permissions are set correctly for all users to have dull rights.
How to reach support (FAQ) - http://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/30400b52-7f26-4ba0-bc18-17e305329d90
-steve
Microsoft MVP Windows Live / Windows Live OneCare, Live Mesh, & MS Security Essentials Forums Moderator