  The quenching of star formation in satellite galaxies is observed over a wide
range of dark matter halo masses and galaxy environments. In the recent Guo et
al (2011) and Fu et al (2013) semi-analytic + N-body models, the gaseous
environment of the satellite galaxy is governed by the properties of the dark
matter subhalo in which it resides. This quantity depends of the resolution of
the N-body simulation, leading to a divergent fraction of quenched satellites
in high- and low-resolution simulations. Here, we incorporate an analytic model
to trace the subhaloes below the resolution limit. We demonstrate that we then
obtain better converged results between the Millennium I and II simulations,
especially for the satellites in the massive haloes ($\rm log
M_{halo}=[14,15]$). We also include a new physical model for the ram-pressure
stripping of cold gas in satellite galaxies. However, we find very clear
discrepancies with observed trends in quenched satellite galaxy fractions as a
function of stellar mass at fixed halo mass. At fixed halo mass, the quenched
fraction of satellites does not depend on stellar mass in the models, but
increases strongly with mass in the data. In addition to the over-prediction of
low-mass passive satellites, the models also predict too few quenched central
galaxies with low stellar masses, so the problems in reproducing quenched
fractions are not purely of environmental origin. Further improvements to the
treatment of the gas-physical processes regulating the star formation histories
of galaxies are clearly necessary to resolve these problems.
