Deploying large language model (LLM)-driven conversational agents in enterprise settings requires prompts that are simultaneously correct at launch and resilient to the non-deterministic behavioral drift that characterizes production LLM deployments. Existing prompt optimization frameworks address prompt quality as a one-time compile-time problem, leaving open the equally critical question of how to detect and repair prompt regressions caused by silent LLM behavior changes over time. We present PRISM (Prompt Reliability via Iterative Simulation and Monitoring), a closed-loop framework that treats prompt engineering as a continuous reliability engineering problem rather than a one-time authorship task. PRISM takes as input plain-language agent requirements, a set of configured tools and memory variables, and an initial draft prompt. It automatically generates test cases from requirements, simulates full multi-turn conversations against a platform-faithful LLM environment, evaluates pass/fail using an LLM-as-judge, diagnoses root causes of failures, and surgically repairs the prompt -- iterating until all tests pass. Critically, PRISM is designed to run on a scheduled basis (daily), treating LLM behavioral drift as a first-class reliability concern. We evaluate PRISM across 35 enterprise conversational agents over a three-week deployment period on the Yellow.ai V3 platform. PRISM reduces median prompt authoring time from 2 days to under 30 minutes, achieves 99% production reliability across all evaluated agents, and successfully identifies and repairs production regressions caused by LLM behavioral drift within a 24-hour detection window. Our results suggest that continuous, simulation-driven prompt optimization is both tractable and necessary for reliable enterprise conversational AI at scale.