Cyber attackers often engage in repeated adaptive attacks, while many existing defensive models are static and lack mechanisms for long-term strategy validation. We introduce a rational verification framework for Repeated Stackelberg Security Games that evaluates the ongoing optimality of defender strategies under rational attacker behaviour. Our framework incorporates discounted payoffs to emphasise early-stage threats and dynamically adjusts strategies in response to evolving conditions. Experimental results show that our approach improves the utility of the defender and supports an effective resource allocation.