Must an isolated completely mixed Nash equilibrium (i.e., all strategies for all players receive positive weight) be essential?

(By essential, I mean the equilibrium z of the game G that for every eps>0 there is delta>0 s.t. if the payoffs of the game are perturbed at most delta to G', then G' has an equilibrium in an eps-neighborhood of z.)

If the answer is no in general - what if the players are binary (i.e., have two actions each)?