Switching a user from normal to admin and back to normal should not affect any of their group permissions from before they were made admin, but if a group has custom permissions, new users by default will have no permission to it.
What I suspect happened is you made a group with custom permissions, then created a new admin, then changed them to normal user. In this case, your observed behavior is exactly what we intend to happen. Think of it this way. That user was always in the None column, but being a site admin gave them a special exception to the normal rules.
Update: FogBugz 8 changed the structure of permissions groups. You now need to check and set the permissions for the user in question on the individual projects. If you use a group to give permissions to a number of projects and the user should be a member of that goup, simply add him/her.