When a site is switched to and from open type to private type, the permissions for the Bookmark portlet resets.
1 User adds an Open Site
2 User clicks site
3 User changes Permissions in Bookmark (flag everything) and saves
4 User changes Site to private
5 User clicks site
6 User verifies Permissions in Bookmark
System resets permissions to default. Changes in step 3 are not kept.
If you start with a closed site and change to an open site the same thing happens.