In many surveillance scenarios, there are some known critical locations where the events of concern are expected to occur. A common goal in such applications is to use sensors to monitor these critical locations with sufficient quality of surveillance within a designated period. However, with limited sensing resources, the coverage and lifetime requirement may not be satisfied at the same time. Thus, sometimes the sensor needs to reduce its duty cycle in order to satisfy the stringent lifetime constraint. In this paper, we model the critical location coverage problem using a point coverage model with the objective of scheduling sensors to maximize the event detection probability while meeting the network lifetime requirement. We show that this problem is NP-hard and propose a distributed algorithm with a provable approximation ratio of 0.5. Extensive simulations show that the proposed distributed algorithm outperforms the extensions of several state-of-the-art schemes with a significant margin while preserving the network lifetime requirement.