We present a survey for metal absorption systems traced by neutral oxygen over 3.2<z<6.5. Our survey uses Keck/ESI and VLT/X-Shooter spectra of 199 QSOs with redshifts up to 6.6. In total, we detect 74 OI absorbers, of which 57 are separated from the background QSO by more than 5000km/s. We use a maximum likelihood approach to fit the distribution of OI{lambda}1302 equivalent widths in bins of redshift and from this determine the evolution in number density of absorbers with W_1302_>0.05{AA}, of which there are 49 nonproximate systems in our sample. We find that the number density does not monotonically increase with decreasing redshift, as would naively be expected from the buildup of metal-enriched circumgalactic gas with time. The number density over 4.9<z<5.7 is a factor of 1.7-4.1 lower (68% confidence) than that over 5.7<z<6.5, with a lower value at z<5.7 favored with 99% confidence. This decrease suggests that the fraction of metals in a low-ionization phase is larger at z~6 than at lower redshifts. Absorption from highly ionized metals traced by CIV is also weaker in higher-redshift OI systems, supporting this picture. The evolution of OI absorbers implies that metal-enriched circumgalactic gas at z~6 is undergoing an ionization transition driven by a strengthening ultraviolet background. This in turn suggests that the reionization of the diffuse intergalactic medium may still be ongoing at or only recently ended by this epoch.