All of the anaerobic environments I can think of are that way because a layer of aerobic life above them separates them from oxygen. If the aerobic life were removed, the anaerobic compartment would equilibriate with the partial pressures of the atmosphere, however slowly, and it would remain at equilibrium until competition between aerobic cells once again pushed the oxygen boundary to the top.
After the great oxygenation event, there was oxygen in the atmosphere but no layers of aerobic life to stop it from diffusing to the bottom of the ocean or deep underground. If there are anaerobic environments that exist independently of aerobic life, our anaerobic ancestors could have survived there until aerobic respiration or tolerance evolved. Otherwise aerobic tolerance would have had to have been present before the great oxygenation event for anything to survive at all.
Which is closer to the truth? (An environment that takes extremely long to equilibriate with the atmosphere, long enough for evolution to be fast in comparison, would count as isolated for the purposes of this question since it would serve as a reservoir of life from which aerobic respiration could emerge.)