A superstabilizing protocol is a protocol that (i) is self-stabilizing, meaning that it can recover from an arbitrarily severe transient fault; and (ii) can recover from a local transient fault while satisfying a passage predicate during recovery. This paper investigates the possibility of superstabilizing protocols for mutual exclusion in a ring of processors, where a local fault consists of any transient fault at a single processor; the passage predicate specifies that there be at most one token in the ring, with the single exception of a spurious token colocated with the transient fault. The first result of the paper is an impossibility theorem for a class of superstabilizing mutual exclusion protocols. Two unidirectional protocols are then presented to show that conditions for impossibility can independently be relaxed so that superstabilization is possible using either additional time or communication registers. A bidirectional protocol subsequently demonstrates that superstabilization in O(1) time is possible. All three superstabilizing protocols are optimal with respect to the number of communication registers used.