Members of boards subject to this chapter are appointed for staggered terms of four years. Except as provided in AS 39.05.080(4), a member of a board serves until a successor is appointed. Except as provided in AS 39.05.080(4), an appointment to fill a vacancy on a board is for the remainder of the unexpired term. A member who has served all or part of two successive terms on a board may not be reappointed to that board unless four years have elapsed since the person has last served on the board.