We study the production amplitude for the reaction $NNto NNpi$ up to next-to-leading order in chiral perturbation theory. We show that the irreducible chiral loops at this order exactly cancel those terms that arise from the off-shell parts of the $pi N$ rescattering vertex. This cancellation is required for formal consistency of the whole scheme. The net effect of the inclusion of all next-to-leading order loops is to enhance the leading rescattering amplitude by a factor of 4/3 compared to phenomenological studies, bringing its contribution to the cross section for $ppto dpi^+$ close to the experimental value.
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