Early stopping promises to reduce compute costs for autonomous coding agents by terminating unpromising runs early. Deciding when to abandon a run requires separating baseline issue difficulty from the trajectory of an individual attempt. We study the distinction in 147,002 execution traces from two public corpora spanning four model-framework settings. Comparing pre-execution issue context against early execution prefixes, we evaluate linear count models, initial-turn text embeddings, task-conditional rankers, and a fine-tuned Qwen3-0.6B monitor. Although early prefixes modestly improve cross-task outcome ranking, within-task discrimination remains near chance across early landmarks (5k-20k tokens): initial-turn embeddings and 20k-token task-conditional models yield AUCs around 0.50, and three-seed neural evaluations across 32,406 attempts at 20k tokens achieve a mean within-task AUC of 0.50 [0.48, 0.51] across tasks of varying solve rates. To evaluate how these predictions translate into stopping decisions, we replay score-guided and matched random restarts under shared token budgets alongside uninterrupted continuation. Under a 75k-token cap, learned restarting improves resolution over matched random restarting by up to 1.98 percentage points. An exact algebraic decomposition resolves this paradox: the gain over random restarting stems almost entirely from between-task stopping allocation (avoiding stops on easy issues), whereas attempt-level selection within a task contributes near zero (-0.11 to +0.24 percentage points). Across all four settings at the 75k cap (and 216 of 224 tested budget-threshold configurations overall), uninterrupted continuation achieves higher solve rates at lower mean token cost than both restart policies. Practical evaluations of early stopping must therefore establish attempt-level discrimination and demonstrate net compute savings relative to continuation.

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