The integration of Artificial Intelligence (AI) into clinical settings presents a software engineering challenge, demanding a shift from isolated models to robust, governable, and reliable systems. However, brittle, prototype-derived architectures often plague industrial applications and a lack of systemic oversight, creating a ``responsibility vacuum'' where safety and accountability are compromised. This paper presents an industry case study of the ``Maria'' platform, a production-grade AI system in primary healthcare that addresses this gap. Our central hypothesis is that trustworthy clinical AI is achieved through the holistic integration of four foundational engineering pillars. We present a synergistic architecture that combines Clean Architecture for maintainability with an Event-driven architecture for resilience and auditability. We introduce the Agent as the primary unit of modularity, each possessing its own autonomous MLOps lifecycle. Finally, we show how a Human-in-the-Loop governance model is technically integrated not merely as a safety check, but as a critical, event-driven data source for continuous improvement. We present the platform as a reference architecture, offering practical lessons for engineers building maintainable, scalable, and accountable AI-enabled systems in high-stakes domains.