We study finite-volume (FV) corrections to determinations of g_A via lattice quantum chromodynamics (QCD) using analytic results and numerical analysis. We observe that SU(2) Heavy Baryon Chiral Perturbation Theory does not provide an unambiguous prediction for the sign of the FV correction, which is not surprising when one also considers large-N_c constraints on the axial couplings. We further show that non-monotonic FV corrections are naturally allowed when one considers either including explicit Δ-resonance degrees of freedom or one works to higher orders in the chiral expansion. We investigate the potential impact of these FV corrections with a precision study of g_A using models of FV corrections that are monotonic and non-monotonic. Using lattice QCD data that is approximately at the 1% level of precision, we do not see significant evidence of non-monotonic corrections. Looking forward to the next phase of lattice QCD calculations, we estimate that calculations that are between the 0.1%-1%-level of precision may be sensitive to these FV artifacts. Finally, we present an update of the CalLat prediction of g_A in the isospin limit with sub-percent precision, g_A^QCD=1.2674(96).