Large Language Models (LLMs) have demonstrated substantial capabilities in conversational AI applications, yet their susceptibility to dialogue breakdowns poses significant challenges to deployment reliability and user trust. This paper introduces a "Detect, Explain, Escalate" framework to manage dialogue breakdowns in LLM-powered agents, emphasizing resource-efficient operation. Our approach integrates two key strategies: (1) We fine-tune a compact 8B-parameter model, augmented with teacher-generated reasoning traces, which serves as an efficient real-time breakdown detector and explainer. This model demonstrates robust classification and calibration on English and Japanese dialogues, and generalizes to the BETOLD dataset, improving accuracy by 7% over its baseline. (2) We systematically evaluate frontier LLMs using advanced prompting (few-shot, chain-of-thought, analogical reasoning) for high-fidelity breakdown assessment. These are integrated into an "escalation" architecture where our efficient detector defers to larger models only when necessary, substantially reducing operational costs and computational overhead. Our fine-tuned model and prompting strategies achieve state-of-the-art performance on DBDC5 and strong results on BETOLD, outperforming specialized classifiers on DBDC5 and narrowing the performance gap to larger proprietary models. The proposed monitor-escalate pipeline reduces inference costs by 54%, providing a cost-effective and interpretable solution for robust conversational AI in high-impact domains. Code and models are publicly available.