Audio deepfake detectors are expected to remain robust to diverse attacks, datasets, and recording conditions, yet collecting training data that cover every future condition is impractical. We investigate whether an already-trained SSL-based detector can improve its generalization through additional recurrent computation, without introducing new training data or updating its original parameters. Directly feeding the encoder output back as its next input, however, severely degrades detection, revealing a mismatch between the representations produced and consumed by a model trained for single-pass inference. We therefore propose CoReLoop, which enables controlled recurrent refinement through loop-specific LoRA and lightweight modules that adapt recurrent inputs, regulate state updates, and align refined representations with the frozen classifier. Across 14 diverse test sets, CoReLoop improves pooled EER across 3-, 6-, 12-, and 24-layer encoders; on the 24-layer model, two-pass refinement reduces EER from 4.85% to 3.74% while training only approximately 11M of 598M parameters. An optional halting head further selects refinement depth per utterance, achieving 3.73% EER with an average of 1.18 passes. Analysis shows that later-pass saturation coincides with smaller applied updates and nearly balanced corrections and regressions, while the recurrent state continues to change.

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