We present high-resolution simulations of an isolated dwarf spheroidal (dSph) galaxy between redshifts z ∼ 10 and z ∼ 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 × 10$\mathrm{<mrow\; data-mjx-texclass="ORD">7</mrow>}$ M⊙ halo, the mass of a typical redshift 10 progenitor of a redshift 0 halo with mass ∼10$\mathrm{<mrow\; data-mjx-texclass="ORD">9</mrow>}$ M⊙. 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 disc-like gas distributions retain more gas than spherical ones, primarily due to the shorter gas cooling times in the disc. 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.