Space Leadership Preservation Act of 2013 - Establishes a six-year term of office for the Administrator of the National Aeronautics and Space Administration (NASA).

Prohibits the Deputy Administrator from acting for, and exercising the powers of, the Administrator for a period exceeding 45 days. Requires the Associate Administrator, after such a 45 day period, to exercise the powers of the Administrator until a new Administrator is appointed and confirmed by the Senate.

Establishes a Board of Directors for NASA.

Sets forth Board membership and appointment criteria. Allows the President to appoint the Administrator and Deputy Administrator from among a list of nominees provided by the Board.

Requires the Board to provide: (1) NASA's proposed annual budget; (2) annual reports on spaceflight infrastructure, unique space capabilities, and the workforce necessary to maintain such infrastructure and capabilities; (3) reports on specific policy matters; and (4) quadrennial reviews of current space programs and a vision for future space exploration.

Authorizes the Administrator to enter into contracts for rocket propulsion systems and manned and unmanned space transportation vehicles and payloads.