Reliability analysis is an important issue in wireless sensor networks (WSNs). This paper aims to study the reliability of a data flow in event-driven wireless sensor networks with multiple sending transmission approach without acknowledgments. 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, the wireless link reliability and the node energy availability are investigated, respectively. Furthermore, the analytical expressions of the instantaneous network reliability and the mean time to failure (MTTF) are derived. Finally, the simulation results validate the correctness and accuracy of the analytical results.