Complex, nitrogen-bearing interstellar molecules, especially amines, are targets of particular interest for detection in star- and planet-forming regions, due to their possible relevance to prebiotic chemistry. However, these NH2-bearing molecules are not universally detected in sources where other, oxygen-bearing complex organic molecules (COMs) are often plentiful. Nevertheless, recent astrochemical models have often predicted large abundances for NH2-bearing complex organics, based on their putative production on dust grains. Here we investigate a range of new gas-phase proton-transfer reactions and their influence on the destruction of COMs. As in past studies, reactions between protonated COMs and ammonia (NH3) are found to be important in prolonging gas-phase COM lifetimes. However, for molecules with proton affinities (PA) greater than that of ammonia, proton-transfer reactions result in drastic reductions in abundances and lifetimes. Ammonia acts as a sink for proton transfer from low-PA COMs, while passing on protons to high-PA species; dissociative recombination with electrons then destroys the resulting ions. Species strongly affected include methylamine (CH3NH2), urea (NH2C(O)NH2) and others bearing the NH2 group. The abundances of these species show a sharp time dependence, indicating that their detectability may rest on the precise chemical age of the source. Rapid gas-phase destruction of glycine (NH2CH2COOH) in the models suggests that its future detection may be yet more challenging than previously hoped.