Wireless Body Area networks (WBANs) have been adopted extensively in academic and industrial research and development in recent years. WBANs promise to provide a suitable environment for remote patient monitoring and enable caregivers to intervene in case of abnormal health conditions. However, WBANs sensors are resource-constrained and face challenges, including, for instance, sensor energy harvesting, efficient routing, parent node selection in case of two hubs links, and data security. The stringent healthcare requirements burden managing WBAN resources and sensor functionality. In this research work, we tackle the issue of total energy consumption, communication overhead, and the lifespan of WBAN. We study the effect of routing and parent node selection on the network lifespan. The study considers a cluster-based routing protocol to establish a WBAN. This approach divides the network into clusters, where each cluster consists of a cluster head called a Relay Node (RN) and a set of functional sensors. Each RN collects data from its sensor nodes and sends it to a base station. However, the relay nodes are susceptible to failures at any time due to the challenging deployment environments and resource constraints of the nodes. In addition, the network sensors are dynamic in positions due to user body movements. Therefore, improving the robustness, fault management, and reliability at different postures becomes necessary. We propose a mobility-aware, energy-efficient Hybrid Fault-Management Clustering Algorithm (HFMCA) adopting the Weighted Bipartite Graph (WBG) to handle the vulnerable RNs prone to failure. The WBG helps find the optimum path between the vulnerable RN and its members to the sink node while maintaining minimum energy consumption and transmission costs. Finally, we conducted extensive experiments, and the simulation results illustrate the proposed algorithm’s efficiency in WBANs regarding energy consumption, network lifespan, and communication overhead.