Extending the lifetime of wireless sensor networks requires energy-conserving operations such as duty-cycling. However, such operations may impact the effectiveness of high-fidelity real-time sensing tasks, such as object tracking, which require high accuracy and short response times. In this paper, we quantify the influence of different duty-cycle schemes on the efficiency of bearings-only object tracking. Specifically, we use the Maximum Likelihood localization technique to analyze the accuracy limits of object location estimates under different response latencies considering variable network density and duty-cycle parameters. Moreover, we study the tradeoffs between accuracy and response latency under various scenarios and motion patterns of the object. We have also investigated the effects of different duty-cycled schedules on the tracking accuracy using acoustic sensor data collected at Aberdeen Proving Ground, Maryland, by the U.S. Army Research Laboratory (ARL).