Airless tires, or non-pneumatic tires (NPTs), offer enhanced durability and eliminate puncture risks, making them a promising alternative to traditional pneumatic tires. However, the fatigue performance of their spoke structures remains a key challenge. This study investigates the fatigue behavior of re-entrant honeycomb auxetic structures using finite element analysis (FEA) in ANSYS Static Structural. A definitive screening design (DSD) was employed with six factors, identifying Young’s modulus as the most significant parameter affecting fatigue life, where higher values reduce longevity. A trade-off between fatigue life and compressive load was observed, requiring an optimization approach. A multiple-response DSD determined that for a target compressive load of 637 N (65 kg), the optimal polymer material should ideally exhibit a Poisson’s ratio of 0.485 and a Young’s modulus of 0.1806 GPa, resulting in a fatigue life of 8,435,847 cycles—exceeding the typical e-scooter lifespan (2 million to 6 million cycles). These findings provide critical insights into auxetic metamaterial design, optimizing structural integrity and fatigue resistance for airless tire applications.