The emerging large language model role-playing agents (LLM RPAs) aim to simulate individual human behaviors, but the persona fidelity is often undermined by manually-created profiles (e.g., cherry-picked information and personality characteristics) without validating the alignment with the target individuals. To address this limitation, our work introduces the Dynamic Persona Refinement Framework (DPRF). DPRF aims to optimize the alignment of LLM RPAs' behaviors with those of target individuals by iteratively identifying the cognitive divergence, either through free-form or theory-grounded, structured analysis, between generated behaviors and human ground truth, and refining the persona profile to mitigate these divergences. We evaluate DPRF with five LLMs on four diverse behavior-prediction scenarios: formal debates, social media posts with mental health issues, public interviews, and movie reviews. DPRF can consistently improve behavioral alignment considerably over baseline personas and generalizes across models and scenarios. Our work provides a robust methodology for creating high-fidelity persona profiles and enhancing the validity of downstream applications, such as user simulation, social studies, and personalized AI.