may be reappointed for terms of six years, but no register shall be reappointed after completion of any term during which he becomes eligible to retire and receive retirement compensation; provided, that a register who becomes eligible to retire during a term shall be eligible to reappointment by the presiding judge of his circuit for not more than six additional terms of one year each; and provided further, that until such time as the register becomes eligible to retire and receive retirement compensation, reappointment shall be automatic unless a majority of the circuit judges within the circuit, or by unanimous agreement where there are only two circuit judges, file a written declaration with the Administrative Director of Courts stating that the register shall not be reappointed. At such time, the office shall be deemed vacant under subsection (a) of this section.