Thematic analysis is difficult to scale: manual workflows are labor-intensive, while fully automated pipelines often lack controllability and transparent evaluation. We present \textbf{CentaurTA Studio}, a web-based system for self-improving human--agent collaboration in open coding and theme construction. The system integrates (1) a two-stage human feedback pipeline separating simulator drafting and expert validation, (2) persistent prompt optimization that distills validated feedback into reusable alignment principles, and (3) rubric-based evaluation with early stopping for process control. Across three domains, CentaurTA achieves the strongest performance in both Open Coding and Theme Construction, reaching up to 92.12\% accuracy and consistently outperforming baseline systems. Agreement between the rubric-based LLM judge and human annotators reaches substantial reliability (average $κ= 0.68$). Ablation studies show that removing the feedback loop reduces performance from 90\% to 81\%, while eliminating the Critic or early stopping degrades accuracy or increases interaction cost. The full system reaches peak performance within 10 iterative rounds (about 25 minutes), demonstrating improved efficiency over expert-only refinement.