  Recent studies have found a dramatic difference between the observed number
density evolution of low mass galaxies and that predicted by semi-analytic
models. While 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 observationally. 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. Firstly, we look for
evidence of a different history of today's low mass galaxies in models and
observations and we find that 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 (sSFR) 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 sSFR 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. [Abridged]
