  We study the production amplitude for the reaction $NN\to NN\pi$ 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 $pp\to d\pi^+$ close to the
experimental value.
