We investigate the evolution of the ionization state of metal-enriched gas in and around galaxies near the epoch of reionization using a sample of 488 metal absorption systems at 4.3 $\lesssim z \lesssim$ 6.3 from the E-XQR-30 survey. We classify the absorption systems based on whether they display only low-ionization absorption (C ii, Si ii, Mg ii), only high-ionization absorption (C iv, Si iv), or both. The percentage of low-ionization-only systems decreases from 24 per cent at $z\sim$ 6 to 2 per cent at $z\sim$ 4.3, whilst the fraction of high-ionization-only systems increases from 52 per cent to 82 per cent. For mixed absorbers (with both low and high ionization absorption), we use the column density ratios log(NC ii/NC iv) and log(NSi ii/NSi iv) to quantify the average ionization as a function of redshift. The log(NSi ii/NSi iv) ratio does not change significantly over 5 $\lesssim z \lesssim$ 6.3. We combine the E-XQR-30 log(NC ii/NC iv) measurements with literature measurements at $z\sim$ 2–4 and find that the log(NC ii/NC iv) ratio declines by a factor of $\sim$20 between $z\sim$ 6 and $z\sim$ 2. To explore possible drivers of this evolution, we run photoionization models of gas slabs illuminated by a uniform ultraviolet (UV) background at fixed density, metallicity, and H i column density. We find that the increase in the ionization state of metal absorbers towards lower redshifts can likely be explained by some combination of (1) an increase in the metallicity of C iv-absorbing gas and (2) a decrease in the typical H i column densities of the absorbing gas, driven by the declining cosmic mean density and a rapid rise in the strength of the UV background during the final stages of reionization.