  We present high resolution simulations of an isolated dwarf spheroidal (dSph)
galaxy between redshifts $z\sim10$ and $z\sim 4$, the epoch when several Milky
Way dSph satellites experienced extended star formation, in order to understand
in detail the physical processes which affect a low-mass halo's ability to
retain gas. It is well-established that supernova feedback is very effective at
expelling gas from a $3\times 10^7$M$_\odot$ halo, the mass of a typical
redshift 10 progenitor of a redshift 0 halo with mass $\sim10^9$M$_\odot$. We
investigate the conditions under which such a halo is able to retain sufficient
high-density gas to support extended star formation. In particular, we explore
the effects of: an increased relative concentration of the gas compared to the
dark matter; a higher concentration dark matter halo; significantly lower
supernova rates; enhanced metal cooling due to enrichment from earlier
supernovae. We show that disk-like gas distributions retain more gas than
spherical ones, primarily due to the shorter gas cooling times in the disk.
However, a significant reduction in the number of supernovae compared to that
expected for a standard initial mass function is still needed to allow the
retention of high density gas. We conclude that the progenitors of the observed
dSphs would only have retained the gas required to sustain star formation if
their mass, concentration and gas morphology were already unusual for those of
a dSph-mass halo progenitor by a redshift of 10.
