This paper investigates the power mode management problem for an IEEE 802.11-based mobile ad hoc network (MANET) that allows mobile hosts to tune to the power-saving (PS) mode. We adopt an asynchronous approach proposed in [26] and correlate this problem to the quorum system concept. We identify a rotation closure property for quorum systems. It is shown that any quorum system that satisfies this property can be translated to an asynchronous power-saving protocol for MANETs. We derive a lower bound for quorum sizes for any quorum system that satisfies the rotation closure property. We identify a group of quorum systems that are optimal or near optimal in terms of quorum sizes, which can be translated to efficient asynchronous power-saving protocols. We also propose a new e-torus quorum system, which can be translated to an adaptive protocol that allows designers to trade hosts' neighbor sensibility for power efficiency.