For the purpose of designing more reliable networks, we extend the traditional reliability analysis from wired networks to wireless networks with imperfect components. This paper aims to study the reliability of a data flow in event-driven wireless sensor networks with acknowledgment-based transmission scheme. Initially, an event-driven wireless sensor network model is described in terms of limited node battery energy and shadowed fading channels. Then, in order to analyze the network reliability, wireless link reliability and node energy availability are investigated, respectively. Further the analytical expressions of the instantaneous network reliability and the mean time to failure are derived. Finally, the simulation results validate the correctness and accuracy of the analytical results.