  Excited-state contamination is one of the dominant uncertainties in lattice
calculations of the nucleon axial-charge, $g_A$. Recently published results in
leading-order chiral perturbation theory (ChPT) predict the excited-state
contamination to be independent of the nucleon interpolator and positive.
However, empirical results from numerical lattice calculations show negative
contamination (downward curvature), indicating that present-day calculations
are not in the regime where the leading-order ChPT predictions apply. In this
paper we show that, under plausible assumptions, one can reproduce the behavior
of lattice correlators by taking into account final-state $N \pi$ interactions,
in particular the effect of the Roper resonance, and by postulating a sign
change in the infinite-volume $N \to N \pi$ axial-vector transition amplitude.
