Physical Unclonable Functions (PUFs) based on Non-Volatile Memory (NVM) technology have emerged as a promising solution for secure authentication and cryptographic applications. By leveraging the multi-level cell (MLC) characteristic of NVMs, these PUFs can generate a wide range of unique responses, enhancing their resilience to machine learning (ML) modeling attacks. However, a significant issue with NVM-based PUFs is their endurance problem; frequent write operations lead to wear and degradation over time, reducing the reliability and lifespan of the PUF. This paper addresses these issues by offering a comprehensive model to predict and analyze the effects of endurance changes on NVM PUFs. This model provides insights into how wear impacts the PUF's quality and helps in designing more robust PUFs. Building on this model, we present a novel design for NVM PUFs that significantly improves endurance. Our design approach incorporates advanced techniques to distribute write operations more evenly and reduce stress on individual cells. The result is an NVM PUF that demonstrates a $62\times$ improvement in endurance compared to current state-of-the-art solutions while maintaining protection against learning-based attacks.