Deploying learned control policies is risky because policies that appear robust in simulation can confidently enter out-of-distribution (OOD) states after Sim-to-Real transfer, causing silent failures and potential hardware damage. Existing anomaly detectors often fail to meet the requirements of high-rate control, extremely low false-positive rates, and interpretable failure feedback. We present \textbf{RAPT} (Recurrent Anomaly Probabilistic Trajectory Model), a lightweight, self-supervised $50$\,Hz deployment monitor that learns nominal execution from large-scale simulation and produces calibrated, per-dimension predictive-deviation signals online. RAPT enables OOD detection under strict false-positive constraints while localizing \emph{when and where} real execution departs from nominal behavior. For post-hoc diagnosis, RAPT combines temporal saliency, joint-kinematic summaries, and LLM-based semantic reasoning to classify likely failure causes in a zero-shot setting. In simulation across four Isaac Lab tasks, RAPT improves TPR by $37\%$ over the strongest baseline at $0.5\%$ episode-level FPR; on hardware, it achieves $89\%$ TPR across $78$ trials with fewer false positives than high-frequency-compatible baselines, and reaches $75\%$ semantic failure diagnosis accuracy across $21$ categories on a challenging OOD subset. Project website, code, and videos: https://humphreymunn.github.io/RAPT/.

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