Oleogelation represents a promising strategy for enhancing the functional and thermal properties of edible oils. This study evaluated the structural protection mechanism of an extra virgin olive oil (EVOO) oleogel, structured with 6% (w/w) beeswax, subjected to prolonged discontinuous deep-frying cycles compared to unstructured EVOO. Degradation kinetics were monitored through total polar compounds (TPCs), acid value, UV absorption, p-anisidine value, and FTIR-ATR spectroscopy. Structural integrity was evaluated via Texture Profile Analysis (TPA), and the thermal trajectory was modeled using Principal Component Analysis (PCA). The results explicitly demonstrate a two-stage kinetic behavior. During the initial phase (Days 1–3), the three-dimensional crystalline network acted as a steric confinement barrier, restricting molecular mobility and oxygen diffusion. This significantly delayed the formation of primary and secondary oxidation products, maintaining TPC and acidity markedly lower than the EVOO control. However, continuous thermal stress induced acute thermomechanical fatigue. By Day 4, the oleogel underwent severe structural collapse—evidenced by a 67% loss in hardness—which abolished the physical barrier and caused the degradation kinetics to accelerate, ultimately converging with those of the unstructured oil. These findings reveal that while beeswax oleogelation substantially boosts initial thermo-oxidative stability, its finite mechanical resistance limits its operational lifespan. Understanding this structural collapse is crucial for engineering more resilient, functionally tailored lipid matrices for high-temperature food applications.