Explainable artificial intelligence (XAI) enables data-driven understanding of factor associations with response variables, yet communicating XAI outputs to laypersons remains challenging, hindering trust in AI-based predictions. Large language models (LLMs) have emerged as promising tools for translating technical explanations into accessible narratives, yet the integration of agentic AI, where LLMs operate as autonomous agents through iterative refinement, with XAI remains unexplored. This study proposes an agentic XAI framework combining SHAP-based explainability with multimodal LLM-driven iterative refinement to generate progressively enhanced explanations. As a use case, we tested this framework as an agricultural recommendation system using rice yield data from 26 fields in Japan. The Agentic XAI initially provided a SHAP result and explored how to improve the explanation through additional analysis iteratively across 11 refinement rounds (Rounds 0-10). Explanations were evaluated by human experts (crop scientists) (n=12) and LLMs (n=14) against seven metrics: Specificity, Clarity, Conciseness, Practicality, Contextual Relevance, Cost Consideration, and Crop Science Credibility. Both evaluator groups confirmed that the framework successfully enhanced recommendation quality with an average score increase of 30-33% from Round 0, peaking at Rounds 3-4. However, excessive refinement showed a substantial drop in recommendation quality, indicating a bias-variance trade-off where early rounds lacked explanation depth (bias) while excessive iteration introduced verbosity and ungrounded abstraction (variance), as revealed by metric-specific analysis. These findings suggest that strategic early stopping (regularization) is needed for optimizing practical utility, challenging assumptions about monotonic improvement and providing evidence-based design principles for agentic XAI systems.