Green hydrogen from solar-powered alkaline water electrolysis (AWE) is pivotal for sustainable energy systems, yet long-term performance predictions often neglect component degradation, leading to overly optimistic feasibility assessments. This paper quantifies the system-level impact of AWE degradation on the lifetime performance of a standalone PV-battery-electrolyzer system. A comprehensive dynamic model was developed, integrating a novel, physics-informed material degradation mechanism based on bubble-induced mechanical stress with coupled sub-models for power generation, storage, and hydrogen production. Comparative "Beginning of Life" (BOL) and 5-year "End of Life" (EOL) simulations were conducted. The results demonstrate that accumulated degradation causes a significant voltage penalty, increasing the AWE cell voltage from 2.0 V to 3.3 V for a 150 W input. In the power-controlled system, this leads to a 41.5% reduction in daily hydrogen throughput. Consequently, the overall solar-to-hydrogen (STH) efficiency collapses from 7.9% at BOL to 4.6% at EOL, an absolute loss of 3.3 percentage points. This study concludes that neglecting AWE degradation leads to a gross overestimation of lifetime productivity, highlighting the necessity of including dynamic aging models in the techno-economic analysis of green hydrogen infrastructure.