Select-then-predict rationalizers expose compact rationale-conditioned predictions, but their generator and predictor can interlock: poor rationales mislead the predictor, while predictor lag or shortcut adaptation sends noisy feedback to the generator. Existing studies reduce this interaction by separating generator search from predictor training, but repeated predictor training is expensive, resulting in poor trade-offs. To address this problem, we propose ReSR (Responsibility-Aware Scheduling for Rationalization), a training-control framework that keeps the standard select-then-predict path while adaptively scheduling generator and predictor updates. ReSR uses online, probe, and reference diagnostics with rationale-structure signals to attribute failures to generator-side rationale quality or predictor lag; a virtual-runtime scheduler then converts this attribution into generator/predictor debts and allocates the next optimization slice. Experiments on Toy and HateXplain show that ReSR improves the accuracy–fidelity–compactness–cost balance: ReSR achieves the best Toy highlight F1 and performance comparable to the state-of-the-art approach on HateXplain highlight F1, while attaining stronger classification performance and substantially lower cost.