(a) A councilman or the mayor shall continue to hold his office until his successor is duly qualified.
(b) A council seat or the mayor's office shall become vacant whenever he is recalled, dies, becomes incapacitated, resigns, refuses to serve, is convicted of a felony, or ceases to be a resident of the town or ward, if elected by ward. A council seat or the mayor's office shall further become vacant upon failure to attend three (3) consecutive regular council meetings unless council for good cause votes to retain him.
(d) If a vacancy occurs in the office of mayor, the council shall call a special election within sixty (60) days to elect a new mayor, unless said vacancy occurs within ninety (90) days of the next regular municipal election. The person elected mayor shall serve in that office until the next regular municipal election.