Algorithmic recourse seeks to provide individuals with actionable recommendations that increase their chances of receiving favorable outcomes from automated decision systems (e.g., loan approvals). While prior research has emphasized robustness to model updates, considerably less attention has been given to the temporal dynamics of recourse--particularly in competitive, resource-constrained settings where recommendations shape future applicant pools. In this work, we present a novel time-aware framework for algorithmic recourse, explicitly modeling how candidate populations adapt in response to recommendations. Additionally, we introduce a novel reinforcement learning (RL)-based recourse algorithm that captures the evolving dynamics of the environment to generate recommendations that are both feasible and valid. We design our recommendations to be durable, supporting validity over a predefined time horizon T. This durability allows individuals to confidently reapply after taking time to implement the suggested changes. Through extensive experiments in complex simulation environments, we show that our approach substantially outperforms existing baselines, offering a superior balance between feasibility and long-term validity. Together, these results underscore the importance of incorporating temporal and behavioral dynamics into the design of practical recourse systems.