Retirenent of a director, appointed in the casual vacancy

According to section 262.

1. In the case of a public company or a private company which is a subsidiary of a public company, if the office of any director appointed by the company in general meeting is vacated before his term of office will expire in the normal course, the resulting casual vacancy may, in default of and subject to any regulations in the articles of the company, be filled by the Board of directors at a meeting of the board.

2. Any person so appointed shall hold office only up to the date up to which the director in whose place he is appointed would have held office if it had not been vacated as aforesaid.

Pursuant to above said provision and if AOA of your company provides, casual vacancy is filled by Board of directors  not by members in general meeting.

if B might have been appointed by board of directors, B's resignation and C's appointment will not fall under filling of casual vacancy, filling of casual vacancy provisions applicable to immediate first persons appointment not to any further appointment.