Specifically, if you assume a partial pressure of Oxygen and of all other gases on the electrode-side of the diffusion membrane, then you'll only see a certain number of "ionization events" per time, and you're limited in how much electrical signal you get by how fast oxygen can diffuse across the membrane. This is likely driven by maintenance of a partial pressure within the membrane. However if you re-ionize the oxygen that you deionized, then the partial pressure is much closer to equilibrium, and therefore the partial pressures are only dependent on the amount of oxygen outside of the membrane instead of being dependent on both the ionization rate and the recovery rate through the membrane. It probably makes the calculation a lot faster and more closely dependent on the environmental presence of oxygen which is what you want.

You're not really making things clearer.

What does "adds back an oxygen molecule" mean?