The cosmic star formation history is known to evolve strongly, by an order of magnitude, out to a redshift about unity. Over the same time period, the average neutral gas density in galaxies evolves only marginally, by a factor of about two. The star formation rate density is high enough that the observed neutral gas in galaxies would be exhausted within about a gigayear in the absence of replenishment, and the question becomes one of what form the replenishment takes. In recent work we have identified a possible mechanism for replenishment that is associated with star formation, supershells within galaxies, which naturally satisfies the requirement that replenishment balances consumption. The dependence of this process on galaxy mass, however, remains an open question and the mass-dependent star formation histories now being measured begin to allow investigation into this aspect of the problem.