While role-playing agents excel in short-term interactions, long-term conversations overwhelm context windows, motivating external memory frameworks. Current systems typically rely on persona-agnostic summarization, which records facts without persona-specific interpretation, yielding generic responses that compromise persona fidelity. To bridge this gap, we introduce RoleMemo, a dataset featuring four reasoning tasks where the factual fragments must be interpreted through the persona to reach the correct answer. Evaluation on RoleMemo exposes critical limitations of persona-agnostic frameworks. We thus propose DualMem, which decouples memory into two streams: factual cognition and persona-conditioned insight. Trained through Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), our framework with a 4B-parameter model outperforms zero-shot persona-agnostic frameworks powered by DeepSeek-V3.2 for sustained persona fidelity. Our resources are available at https://github.com/role2026/rolememo.