Measurements of the neutral hydrogen gas content of a sample of 93 post-merger galaxies are presented, from a combination of matches to the ALFALFA.40 data release and new Arecibo observations. By imposing completeness thresholds identical to that of the ALFALFA survey, and by compiling a mass-, redshift- and environment-matched control sample from the public ALFALFA.40 data release, we calculate gas fraction offsets (Delta f_gas) for the post-mergers, relative to the control sample. We find that the post-mergers have HI gas fractions that are consistent with undisturbed galaxies. However, due to the relative gas richness of the ALFALFA.40 sample, from which we draw our control sample, our measurements of gas fraction enhancements are likely to be conservative lower limits. Combined with comparable gas fraction measurements by Fertig et al. in a sample of galaxy pairs, who also determine gas fraction offsets consistent with zero, we conclude that there is no evidence for significant neutral gas consumption throughout the merger sequence. From a suite of 75 binary merger simulations we confirm that star formation is expected to decrease the post-merger gas fraction by only 0.06 dex, even several Gyr after the merger. Moreover, in addition to the lack of evidence for gas consumption from gas fraction offsets, the observed HI detection fraction in the complete sample of post-mergers is twice as high as the controls, which suggests that the post-merger gas fractions may actually be enhanced. We demonstrate that a gas fraction enhancement in post-mergers, relative to a stellar mass-matched control sample, would indeed be the natural result of merging randomly drawn pairs from a parent population which exhibits a declining gas fraction with increasing stellar mass.