Reason for no change in electrode potential in reference electrodes

Reference electrodes such as the saturated calomel electrode and silver chloride electrode have a constant potential because the $ce{Cl-}$ concentration (or, to be more precise, the activity) is constant.
The semi-reaction for those electrodes are:

$$ce{Hg2Cl2 + 2e- <=> 2Hg + 2Cl-}$$

$$ce{AgCl + e- <=> Ag + Cl-}$$

Now, since chloride ions are produced (or consumed, when the electrode is an anode) from the half-reactions, how is it possible that their concentration remains constant?

Is the quantity of chloride produced or consumed is negligible compared to that coming from the $ce{KCl}$ dissociation?