Early failure alerting requires deciding, while a dialog or agent trajectory unfolds, whether it is likely to fail. Existing approaches broadly follow two directions. LLM-based uncertainty monitoring either elicits confidence from the acting model, tying reliability to its own self-assessment, or queries an external frontier judge at each prefix, incurring costly repeated inference. Trained monitors instead either rely on per-turn annotations, which are rarely available, or train every prefix to predict the terminal outcome without explicitly modeling where failure-indicating evidence appears. We address these limitations with a lightweight external monitor trained only from trajectory-level outcomes, motivated by a pattern across five benchmarks: turns rated highly relevant to failure are sparse and often late. Its attention-based multiple instance learning (MIL) component learns turn-level contributions from trajectory outcomes and distills them into online evidence features that complement prefix predictions. We pair the resulting failure estimates with $α$-STOP, a single preference-conditioned policy that selects accuracy-earliness operating points at inference time. The predictor improves Pareto-frontier quality (hypervolume) by 1-10% over naive prefix supervision, while the full system improves it by 3-42% over state-of-the-art trigger policies without per-preference retraining. By avoiding repeated frontier-model calls, our lightweight monitor reduces measured per-decision serving cost by 1,103-3,749$\times$ and latency by 31-106$\times$ relative to the LLM-based uncertainty monitor (GPT-5.2).

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