We study the problem of tracking an object that is moving randomly through a dense network of wireless sensors. We assume that each sensor has a limited range for detecting the presence of the object, and that the network is sufficiently dense so that the sensors cover the area of interest. In order to conserve energy the sensors may be put into a sleep mode with a timer that determines the sleep duration. We assume that a sensor that is asleep cannot be communicated with or woken up. Thus the sleep duration needs to be determined at the time the sensor goes to sleep based on all the information available to the sensor. The objective is to track the location of the object to within the accuracy of the range of the sensor. However, having sleeping sensors in the network could result in tracking errors, and hence there is a tradeoff between the energy savings and the tracking error that results from the sleeping actions at the sensors. We consider the design of sleeping policies that optimize this tradeoff.