Hi Robin & Henry,
Button visibility is controlled by WebDir, so if the buttons are not showing up it is probably not caused by service account permisions. However, if the buttons are visible but the members are never added or removed then I would suspect service account permissions.
Is the problem consistent or intermittent? For example, if User A is the owner of Group 1 and Group 2, is User A always unable to manage Group 1 or just sometimes? Is User A able to manage Group B? Are User A, Group 1 and group Group 2 int he same domain/forest?
--Robert