Recent studies have found a dramatic difference between the observed number density evolution of low-mass galaxies and that predicted by semi-analytic models. Whilst models accurately reproduce the z = 0 number density, they require that the evolution occurs rapidly at early times, which is incompatible with the strong late evolution found in observational results. We report here the same discrepancy in two state-of-the-art cosmological hydrodynamical simulations, which is evidence that the problem is fundamental. We search for the underlying cause of this problem using two complementary methods. First, we consider a narrow range in stellar mass of log (Mstar/(h−2 M⊙)) = 9–9.5 and look for evidence of a different history of today's low-mass galaxies in models and observations. We find that the exclusion of satellite galaxies from the analysis brings the median ages and star formation rates of galaxies into reasonable agreement. However, the models yield too few young, strongly star-forming galaxies. Secondly, we construct a toy model to link the observed evolution of specific star formation rates with the evolution of the galaxy stellar mass function. We infer from this model that a key problem in both semi-analytic and hydrodynamical models is the presence of a positive instead of a negative correlation between specific star formation rate and stellar mass. A similar positive correlation is found between the specific dark matter halo accretion rate and the halo mass, indicating that model galaxies are growing in a way that follows the growth of their host haloes too closely. It therefore appears necessary to find a mechanism that decouples the growth of low-mass galaxies, which occurs primarily at late times, from the growth of their host haloes, which occurs primarily at early times. We argue that the current form of star formation-driven feedback implemented in most galaxy formation models is unlikely to achieve this goal, owing to its fundamental dependence on host halo mass and time.