This paper proposes StratMamba, a dual-stream Mamba-based temporal modeling architecture, to more efficiently capture long-horizon temporal dependencies required for robot navigation in complex and obstacle-rich environments. StratMamba leverages a combination of fast-decay and slow-decay memory architectures, where the fast-decay component processes high-frequency LiDAR data for reactive obstacle avoidance, while the slow-decay component maintains longer-horizon goal information for strategic planning. We perform extensive evaluations of different obstacle avoidance scenarios in IsaacLab and Gazebo, while also validating successful sim-to-real deployment on a Unitree GO1 quadruped robot navigating in the presence of static/dynamic obstacles. Comparisons with other temporal RL baselines, such as LSTM, Transformer, and Vanilla-Mamba, show that our StratMamba achieves exceptional temporal reasoning efficiency with a lower timeout rate, while maintaining the fastest navigation speed (576 median steps, 5.0% better than Vanilla-Mamba). It also achieves the highest path optimality (0.915 path efficiency) across all baselines. Real-world evaluation reveals that StratMamba maintains more robust performance across extended LiDAR ranges compared to vanilla Mamba and the Transformer, demonstrating that dual-stream partitioning effectively balances reactive safety with strategic navigation under challenging sensing conditions.

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