You may need to add removed constituents to a group sometimes, like if you are trying to have support re-activate those constituents. However, you cannot add a removed constituent to a group by going into the group and using the "Add Members" function. Instead you will want to add the member to the group by going to their profile and following these steps:
  1. Go to their "Groups" tab
  2. Click on "Edit Group Membership"
  3. Choose the group you want to add the constituent to and click "Save"