Members of the Board shall hold office until their respective successors have been appointed and qualified. Any member may resign from his or her office, to take effect when his or her successor has been appointed and has qualified. The Governor and the county boards may remove any member of the Board appointed by them in case of incompetency, neglect of duty, or malfeasance in office. They shall give the member a copy of the charges against him or her and an opportunity to be publicly heard in person or by counsel in his or her own defense upon not less than 10 days’ notice. In case of failure to qualify within the time required, of abandonment of office, or of death, conviction of a crime, or removal from office, the office shall become vacant. Each vacancy shall be filled for the unexpired term by appointment in like manner, and with like regard as to the place of residence of the appointee, as in case of expiration of the term of a member of the Board.