While Large Language Models (LLMs) have achieved remarkable success in Text-to-SQL tasks, their deployment in real-world environments is hindered by latent reliability issues. Identifying these latent weaknesses is critical for building trustworthy database interfaces, yet current diagnostic approaches rely heavily on static, expert-defined rules, which lack the capability for systematic and automated exploration. To bridge this gap, we propose SAGE (Systematic Automated Guided Exploration), a novel framework designed to autonomously uncover latent failure patterns in LLM-based Text-to-SQL generation. Specifically, SAGE generates vulnerability hypotheses for given samples and references a continuously evolving Vulnerability Codex to design targeted perturbations, thereby iteratively verifying and documenting potential defects. Extensive experiments on state-of-the-art open-source LLMs demonstrate that SAGE uncovers a substantial number of failure cases, highlighting the significant fragility of current models. Furthermore, our analysis reveals that the Vulnerability Codex exhibits strong cross-model transferability, indicating that the discovered patterns represent generalized structural weaknesses. Finally, we explore SAGE’s potential for remediation. Furthermore, a preliminary attempt at lightweight fine-tuning on the generated samples yields promising improvements, suggesting a scalable pathway for closing the reliability loop in future work.