The problem considered is that of tracking an object that is moving through a dense network of wireless sensors. Each sensor has a limited range for detecting the presence of the object and the goal is to track the location of the object to within the accuracy of the range of the sensor. The network is assumed to be sufficiently dense so that the sensors cover the entire area of interest. The object is assumed to follow a random path through the sensor field whose statistics are assumed to be known a priori. It is assumed that in order to conserve energy the sensors go into sleep mode periodically. The sleep duration is determined at the time the sensor goes to sleep based on the information available to the sensor. It is assumed that a sensor that is asleep cannot be communicated with or woken up prematurely. Having sleeping sensors in the network could result in tracking errors, and hence there is a natural tradeoff between energy savings and tracking error. This paper considers the design of sleeping policies with the goal of optimizing this tradeoff.