This paper proposes a fault tolerant permission-based k-mutual exclusion algorithm which does not rely on timers, nor on failure detectors, neither does it require extra messages for detecting node failures. Fault tolerance is integrated in the algorithm itself and it is provided if the underlying system guarantees the Responsiveness Property (RP). Based on Raymond's algorithm, our algorithm exploits the request-reply messages exchanged by processes to get access to one of the k units of the shared resource in order to dynamically detect failures and adapt the algorithm to tolerate them.