Although Sparse Autoencoders (SAEs) have mitigated the opacity of large language models (LLMs) by decomposing dense representations into sparse features, explaining these features still remains a central challenge. Current explanation methods, however, typically operate within an open-loop paradigm, failing to leverage mechanistic feedback for further refinement. In this paper, we propose SAEExplainer, a training framework utilizes activation scores as an objective reward signal to train the model for self-correction and iterative bootstrapping. By iteratively verifying and correcting foundational explanations through a two-round optimization process, SAEExplainer achieves continuous improvement in its explanatory capabilities. This mechanism significantly reduces explanation hallucinations and reinforces causal triggering patterns. Extensive experiments demonstrate our approach improves upon established baselines across most metrics, especially in causal triggering and discriminative activation.