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. For the observed neutral hydrogen mass density to remain constant or only slowly evolving, the replenishment must balance the consumption. Observations of gas infall and outflows in nearby galaxies suggest there may be insufficient infalling material to balance the consumption, though, raising the question of whether a new mechanism for replenishment may be required. We present a mechanism for replenishment that is associated with star formation, supershells within galaxies, and discuss the advantages and limitations of this mechanism.