  We simulate the evolution of a 10^9 Msun dark matter halo in a cosmological
setting with an adaptive-mesh refinement code as an analogue to local low
luminosity dwarf irregular and dwarf spheroidal galaxies. The primary goal of
our study is to investigate the roles of reionization and supernova feedback in
determining the star formation histories of low mass dwarf galaxies. We include
a wide range of physical effects, including metal cooling, molecular hydrogen
formation and cooling, photoionization and photodissociation from a
metagalactic background, a simple prescription for self-shielding, star
formation, and a simple model for supernova driven energetic feedback. We carry
out simulations excluding each major effect in turn. We find that reionization
is primarily responsible for expelling most of the gas in our simulations, but
that supernova feedback is required to disperse the dense, cold gas in the core
of the halo. Moreover, we show that the timing of reionization can produce an
order of magnitude difference in the final stellar mass of the system. For our
full physics run with reionization at z=9, we find a stellar mass of about 10^5
Msun at z=0, and a mass-to-light ratio within the half-light radius of
approximately 130 Msun/Lsun, consistent with observed low-luminosity dwarfs.
However, the resulting median stellar metallicity is 0.06 Zsun, considerably
larger than observed systems. In addition, we find star formation is truncated
between redshifts 4 and 7, at odds with the observed late time star formation
in isolated dwarf systems but in agreement with Milky Way ultrafaint dwarf
spheroidals. We investigate the efficacy of energetic feedback in our simple
thermal-energy driven feedback scheme, and suggest that it may still suffer
from excessive radiative losses, despite reaching stellar particle masses of
about 100 Msun, and a comoving spatial resolution of 11 pc.
