  Comparison of observed satellite galaxies of the Milky Way (hereafter MW)
with dark matter subhaloes in cosmological $N$-body simulations of MW-mass
haloes suggest that such subhaloes, if they exist, are occupied by satellites
in a stochastic fashion. We examine how inefficient massive star formation and
associated supernova feedback in high-redshift progenitors of present-day
low-mass subhaloes might contribute to this stochasticity. Using a Monte Carlo
approach to follow the assembly histories of present-day low-mass haloes with
$10^7 \lesssim M \leq 10^{10}$ ${\rm M}_{\odot}$, we identify when cooling and
star formation is likely to proceed, and observe that haloes with present-day
masses $\lesssim 10^9 {\rm M}_{\odot}$ never grow sufficiently massive to
support atomic hydrogen line cooling. Noting that the star formation timescale
decreases sharply with stellar mass as $t_{\rm PMS} \propto m_{\ast}^{-2.5}$,
we argue that, should the conditions for high mass star formation arise in
low-mass haloes, the ensuing supernovae are likely to disrupt ongoing
lower-mass star formation and unbind gas within the halo. This potentially
star-forming gas is unlikely to be replenished in lower mass haloes because of,
e.g. cosmological reionization, and so we expect galaxy formation to be stymied
in a manner that depends on host halo assembly history and the efficiency and
timing of star formation in proto-galaxies, which we illustrate using a Monte
Carlo model. Based on these simple physical arguments, we assert that
stochasticity of star formation and feedback is an essential but overlooked
ingredient in modelling galaxy formation on the smallest scales.
