Failure is inevitable for embodied navigation in complex environments. To enhance the resilience, replanning (RP) is a viable option, where the robot is allowed to fail, but is capable of adjusting plan until success. However, existing RP approaches freeze the ego action model and miss the opportunities to explore better plans by upgrading the robot itself. To address this limitation, we propose Self-Evolutionary RePlanning, or SERP for short, which leads to a paradigm shift from frozen models towards evolving models by run-time learning from recent experiences. In contrast to existing model evolution approaches that often get stuck at predefined static parameters, we introduce agentic self-evolving action model that uses in-context learning with auto-differentiation (ILAD) for adaptive function adjustment and global parameter reset. To achieve token-efficient replanning for SERP, we also propose graph chain-of-thought (GCOT) replanning with large language model (LLM) inference over distilled graphs. Extensive simulation and real-world experiments demonstrate that SERP achieves higher success rate with lower token expenditure over various benchmarks, validating its superior robustness and efficiency across diverse environments.