Whenever a vacancy exists in any position in the service of the city, it shall be filled by appointment of one of the three persons who rank highest on the appropriate eligible register of the board or by transfer within the service of the city from another position of the same class. However, the ranking layoff of the same class shall be appointed in every instance. Whenever it is impossible for the board to certify eligible persons to a vacancy, the board may authorize the appointing authority to fill the vacancy temporarily pending the establishment of an eligible register. No such authorization may be given for longer than 120 days, and no such employee shall have status under this part. All appointments, other than temporary appointments, shall be probationary for six months from the date of appointments. A probationary subordinate employee may be discharged by his or her appointing authority for unsatisfactory service at any time before the expiration of that period if the action is approved by the board; a probationary department head employee may be discharged or demoted similarly by his or her appointing authority upon approval by the board. After the expiration of the probationary period, an appointment shall become permanent.