I posted about this a few times here. More Here and Here. This problem no longer affects my installation but it looks like Microsoft has released a fix. The December cumulative updates for SharePoint state the following as an issue they fix:
When you try to perform a search in a Windows SharePoint Services 3.0 site, the “This List: Name of list, doclib etc.” scope for a list is missing. This issue occurs because https:// is used to visit the Windows SharePoint Services 3.0 site.
That looks an awful lot like what we were experiencing. If you are still seeing this issue, try installing the latest updates and let us know if it fixes it.
Go HERE to get the updates.