We present a detailed assessment of the global atomic hydrogen gas fraction (fgas = log[MHI/M*]) in a sample of post-merger galaxies identified in the Sloan Digital Sky Survey (SDSS). Archival HI measurements of 47 targets are combined with new Arecibo observations of a further 51 galaxies. The stellar mass range of the post-merger sample, our observing strategy, detection thresholds and data analysis procedures replicate those of the extended GALEX Arecibo SDSS Survey (xGASS) which can therefore be used as a control sample. Our principal results are (1) the post-merger sample shows a ~50 per cent higher HI detection fraction compared with xGASS; (2) accounting for non-detections, the median atomic gas fraction of the post-merger sample is larger than the control sample by 0.3-0.6 dex; and (3) the median atomic gas fraction enhancement (Δfgas), computed on a galaxy-by-galaxy basis at fixed stellar mass, is 0.51 dex. Our results demonstrate that recently merged galaxies are typically a factor of ~3 more HI rich than control galaxies of the same M*. If the control sample is additionally matched in star formation rate, the median HI excess is reduced to Δfgas = 0.2 dex, showing that the enhanced atomic gas fractions in post-mergers are not purely a reflection of changes in star formation activity. We conclude that merger-induced starbursts and outflows do not lead to prompt quenching via exhaustion/expulsion of the galactic gas reservoirs. Instead, we propose that if star formation ceases after a merger, it is more likely due to an enhanced turbulence which renders the galaxy unable to effectively form new stars.