Sustained casing pressure (SCP) is a primary indicator of well integrity degradation, arising from compromised barriers such as cement, casing, tubing/packer components, or wellhead seals. Traditional SCP diagnostics—based on manual interpretation of annular pressure trends, bleed-off tests, and operational records—are often time-consuming, analyst-dependent, and difficult to scale across large well populations. This study presents a physics-informed machine learning (PIML) framework that integrates engineering-based physical principles, including fluid compressibility, thermal expansion, and leak-path mechanics, into a machine learning workflow for automated and scalable SCP classification. The framework is applied to field monitoring data from 26 wells, with detailed multi-annulus case studies for wells A5, A8, and A12. The method classifies cycle-level SCP behavior into six diagnostic types—no pressure, thermal pressure, trapped pressure, recharge pressure, constant pressure, and high-rate recharge—and maintains physically plausible and interpretable outputs under noisy or complex pressure signatures. Operationally, the framework supports real-time, SCADA-integrated surveillance to enable early detection of integrity threats, prioritization of higher-risk wells, and proactive intervention planning. The novelty of this work lies in embedding physical constraints directly into the classification logic, producing a robust and interpretable diagnostic capability that advances SCP analysis from a reactive, manual task toward automated well-integrity surveillance applicable to offshore, HPHT, CO2 sequestration, and hydrogen storage operations.