Robot learning methods have recently made great strides, but generalization and robustness challenges still hinder their widespread deployment. Failing to detect and address potential failures renders state-of-the-art learning systems not combat-ready for high-stakes tasks. Recent advances in interactive imitation learning have presented a promising framework for human-robot teaming, enabling the robots to operate safely and continually improve their performances over long-term deployments. Nonetheless, existing methods typically require constant human supervision and preemptive feedback, limiting their practicality in realistic domains. This work aims to endow a robot with the ability to monitor and detect errors during task execution. We introduce a model-based runtime monitoring algorithm that learns from deployment data to detect system anomalies and anticipate failures. Unlike prior work that cannot foresee future failures or requires failure experiences for training, our method learns a latent-space dynamics model and a failure classifier, enabling our method to simulate future action outcomes and detect out-of-distribution and high-risk states preemptively. We train our method within an interactive imitation learning framework, where it continually updates the model from the experiences of the human-robot team collected using trustworthy deployments. Consequently, our method reduces the human workload needed over time while ensuring reliable task execution. Our method outperforms the baselines across system-level and unit-test metrics, with 23% and 40% higher success rates in simulation and on physical hardware, respectively.