Abstract: Large language model (LLM) agents increasingly combine reasoning, tool use, and action, but most evidence comes from episodic tasks with relatively immediate feedback and reset failures. Long-running physical control operates in a different regime: actions alter future states, errors compound across decisions, and an agent must improve from experience without being allowed to rewrite the physical rules that make execution safe. We study this regime through irrigation, where daily decisions interact with soil-water dynamics over entire growing seasons. We present Mimir, a physics-grounded LLM agent organized around two repair timescales. At the fast timescale, a structured physical interface and deterministic simulator turn an LLM output into a proposal that we numerically check, revise, and subject to bounded deterministic action selection before execution. At the slow timescale, recurrent failure patterns are consolidated into persistent contextual principles that condition future proposals, while the physical model, evaluator, and execution constraints remain immutable. Under a common retrospective evaluator across multiple sites, crops, and years, Mimir attains the lowest reported aggregate control cost among the evaluated references and uses about 51% less irrigation than the historical schedule replay. The ablation study show higher control cost when forward simulation, verified revision, or persistent context is removed; model-scale and model-family studies show no monotonic gain from increasing LLM size. The resulting lesson show that persistent physical agents can combine semantic reasoning with bounded, evidence-driven self-improvement while reserving physical truth and actuator authority for explicit numerical mechanisms.