Wireless Sensor Networks (WSNs) has made significant advancements in various areas and are increasingly being integrated into larger IoT ecosystems, enabling seamless connectivity and data exchange between sensors enhancing the scalability and functionality allowing for diverse applications. This integration improves the reliability, adaptability, and effectiveness of WSNs, allowing for a wide range of applications such as smart cities, industrial automation, environmental monitoring, and healthcare systems. Despite these developments, energy efficiency and fault detection still continue to be significant considerations for WSN reliability. Timely detection and diagnosis of faults are essential to maintain network performance, prevent data loss, and reduce downtime. Duty cycling has emerged as a key strategy for energy-efficient operation in WSNs reducing idle consumption of energy while retaining adequate network responsiveness to detect and respond to issues. Duty cycling enables adaptive resource management, as active and sleep durations can be dynamically modified in response to network demand, sensor failure rates. The proposed methodology provides a comprehensive study aimed at understanding the interplay between energy consumption and system failures in WSNs with the implementation of queueing theory, where sensor nodes alternate between active and sleep states during the breakdown state to reduce power consumption. Using generating function technique explicit transient state probabilities of various stages of power management modes are computed to evaluate system performance metrics, such as response times, busy and idle state probabilities and recovery rates. Numerical findings reveal that well designed duty cycles can greatly enhance energy consumption while preserving fault detection capabilities, underlining the need of adaptive power management in ensuring reliable WSN operations.