Long-term performance predictions for solar-powered alkaline water electrolyzers (AWE) often neglect material degradation, leading to optimistic techno-economic assessments. This paper presents a degradation-aware analysis to identify an optimal operating strategy that maximizes the lifetime value of a standalone PV-battery-AWE system. A comprehensive dynamic model, incorporating a physics-informed degradation mechanism, was used to simulate ten distinct operational power strategies (25 W to 250 W) over a 5-year period. The results reveal a critical trade-off between throughput and longevity. The aggressive 250 W strategy incurred over 14 times more degradation than the 25 W strategy, resulting in a 52% loss in its daily hydrogen production rate by the end of life. While this aggressive strategy yielded the highest cumulative production (107.6 kg) and lifetime revenue ($430.4), it showed severely diminishing returns compared to less intensive strategies. The analysis demonstrates that the optimal strategy is not simply the one with the highest initial output. This study concludes that a degradation-aware approach is essential for accurately forecasting the lifetime value and identifying the most economically sustainable operating strategy for green hydrogen systems.