  Using high resolution hydrodynamical cosmological simulations, we study the
gas accretion history of low mass halos located in a field-like, low density
environment. We track their evolution individually from the early,
pre-reionization era, through reionization, and beyond until $z=0$. Before
reionization, low mass halos accrete cool cosmic web gas at a very rapid rate,
often reaching the highest gas mass they will ever have. But when reionization
occurs, we see that almost all halos lose significant quantities of their gas
content, although some respond less quickly than others. We find that the
response rate is influenced by halo mass first, and secondarily by their
internal gas density at the epoch of reionization. Reionization also fully
ionises the cosmic web gas by z$\sim$6. As a result, the lowest mass halos
(M$\sim$10$^6~h^{-1}$M$_\odot$ at $z=6$) can never again re-accrete gas from
the cosmic web, and by $z\sim5$ have lost all their internal gas to ionisation,
resulting in a halt in star formation at this epoch. However, more massive
halos can recover from their gas mass loss, and re-accrete ionised cosmic web
gas. We find the efficiency of this re-accretion is a function of halo mass
first, followed by local surrounding gas density. Halos that are closer to the
cosmic web structure can accrete denser gas more rapidly. We find that our
lower mass halos have a sweet spot for rapid, dense gas accretion at distances
of roughly 1-5 virial radii from the most massive halos in our sample
($>$10$^8~h^{-1}$M$_\odot$), as these tend to be embedded deeply within the
cosmic web.
