We present a survey for low-ionization metal absorption line systems towards 17 QSOs at redshifts z _ { em } = 5.8 - 6.4 . Nine of our objects were observed at high resolution with either Keck/HIRES or Magellan/MIKE , and the remainder at moderate resolution with Keck/ESI . The survey spans 5.3 < z _ { abs } < 6.4 and has a pathlength interval \Delta X = 39.5 , or \Delta z = 8.0 . In total we detect ten systems , five of which are new discoveries . The line-of-sight number density , \ell ( X ) = 0.25 ^ { +0.21 } _ { -0.13 } ( 95 % confidence ) , is consistent with the combined number density at z \sim 3 of DLAs and sub-DLAs , which comprise the main population of low-ionization systems at lower redshifts . This apparent lack of evolution may occur because low ionization systems are hosted by lower-mass halos at higher redshifts , or because the mean cross section of low-ionization gas at a given halo mass increases with redshift due to the higher densities and lower ionizing background . The roughly constant number density notably contrasts with the sharp decline at z > 5.3 in the number density of highly-ionized systems traced by C iv . The low-ionization systems at z \sim 6 span a similar range of velocity widths as lower-redshift sub-DLAs but have significantly weaker lines at a given width . This implies that the mass-metallicity relation of the host galaxies evolves towards lower metallicities at higher redshifts . These systems lack strong Si iv and C iv , which are common among lower-redshift DLAs and sub-DLAs . This is consistent , however , with a similar decrease in the metallicity of the low- and high-ionization phases , and does not necessarily indicate a lack of nearby , highly-ionized gas . The high number density of low-ionization systems at z \sim 6 suggests that we may be detecting galaxies below the current limits of i -dropout and Ly \alpha  emission galaxy surveys . These systems may therefore be the first direct probes of the ‘ typical ’ galaxies responsible for hydrogen reionization .