From the first published z>3 survey of 21-cm absorption within the hosts of radio galaxies and quasars, Curran et al. (2008b) found an apparent dearth of cool neutral gas at high redshift. From a detailed analysis of the photometry, each object is found to have a 1216 Angstrom continuum luminosity in excess of L > 1e23 W/Hz, a critical value above which 21-cm has never been detected at any redshift. For a variety of gas density distributions, we show that by placing a quasar within a galaxy of gas there is always an ultra-violet luminosity above which all of the gas in the galaxy is excited (and most likely ionised). Above this critical luminosity the hydrogen cannot be detected in the absorption of the 21-cm transition (and possibly Lyman-alpha) and while in this state the gas cannot engage in star formation. Applying the mean ionising photon rate of all of the sources searched, we find, using canonical values for the gas density and recombination rate coefficient, that the observed critical luminosity gives a scale-length (3 kpc) similar that of the neutral hydrogen (HI) in the Milky Way, a large spiral galaxy. This demonstrates that these galaxies are truly devoid of star-forming material, rather the non-detection of 21-cm being due to the sensitivity limits of current radio telescopes.