Objective: Large language models (LLMs) show promise for clinical discharge planning, but their use is constrained by hallucination, omissions, and miscalibrated confidence. We introduce a self-improving, cache-optional Planner-Auditor framework that improves safety and reliability by decoupling generation from deterministic validation and targeted replay. Materials and Methods: We implemented an agentic, retrospective, FHIR-native evaluation pipeline using MIMIC-IV-on-FHIR. For each patient, the Planner (LLM) generates a structured discharge action plan with an explicit confidence estimate. The Auditor is a deterministic module that evaluates multi-task coverage, tracks calibration (Brier score, ECE proxies), and monitors action-distribution drift. The framework supports two-tier self-improvement: (i) within-episode regeneration when enabled, and (ii) cross-episode discrepancy buffering with replay for high-confidence, low-coverage cases. Results: While context caching improved performance over baseline, the self-improvement loop was the primary driver of gains, increasing task coverage from 32% to 86%. Calibration improved substantially, with reduced Brier/ECE and fewer high-confidence misses. Discrepancy buffering further corrected persistent high-confidence omissions during replay. Discussion: Feedback-driven regeneration and targeted replay act as effective control mechanisms to reduce omissions and improve confidence reliability in structured clinical planning. Separating an LLM Planner from a rule-based, observational Auditor enables systematic reliability measurement and safer iteration without model retraining. Conclusion: The Planner-Auditor framework offers a practical pathway toward safer automated discharge planning using interoperable FHIR data access and deterministic auditing, supported by reproducible ablations and reliability-focused evaluation.