Lifetime maximization is one key element in the design of sensor-network-based surveillance applications. We propose a protocol for node sleep scheduling that guarantees a bounded-delay sensing coverage while maximizing network lifetime. Our sleep scheduling ensures that coverage rotates such that each point in the environment is sensed within some finite interval of time, called the detection delay. The framework is optimized for rare event detection and allows favorable compromises to be achieved between event detection delay and lifetime without sacrificing (eventual) coverage for each point. We compare different sleep scheduling policies in terms of average detection delay, and show that ours is closest to the detection delay lower bound for stationary event surveillance. We also explain the inherent relationship between detection delay, which applies to persistent events, and detection probability, which applies to temporary events. Finally, a connectivity maintenance protocol is proposed to minimize the delay of multi-hop delivery to a base-station. The resulting sleep schedule achieves the lowest overall target surveillance delay given constraints on energy consumption.