ReRAM-based accelerators exhibit enormous potential to increase computational efficiency for DNN inference tasks, delivering significant performance and energy savings over traditional platforms. By incorporating adaptive scheduling, these accelerators dynamically adjust to DNN requirements, optimizing allocation of constrained hardware resources. However, ReRAM cells have limited endurance cycles due to wear-out from multiple updates for each inference execution, which shortens the lifespan of ReRAM-based accelerators and presents a practical challenge in positioning them as alternatives to conventional platforms like TPUs. Addressing these endurance limitations is essential for making ReRAM-based solutions viable for long-term, high-performance DNN inference. To address the lifespan limitations of ReRAM-based accelerators, we introduce Hamun, an approximate computing method designed to extend the lifespan of ReRAM-based accelerators through a range of optimizations. Hamun incorporates a novel mechanism that detects faulty cells due to wear-out and retires them, avoiding in this way their otherwise adverse impact on DNN accuracy. Moreover, Hamun extends the lifespan of ReRAM-based accelerators by adapting wear-leveling techniques across various abstraction levels of the accelerator and implementing a batch execution scheme to maximize ReRAM cell usage for multiple inferences. Additionally, Hamun introduces a new approximation method that leverages the fault tolerance characteristics of DNNs to delay the retirement of worn-out cells, reducing the performance penalty of retired cells and further extending the accelerator’s lifespan. On average, evaluated on a set of popular DNNs, Hamun demonstrates an improvement in lifespan of 13.2x over a state-of-the-art baseline. The main contributors to this improvement are the fault handling and batch execution schemes, which provide 4.6x and 2.6x lifespan improvements respectively.