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For achieving strict closed-loop system performance guarantees in the presence of exogenous disturbances and system uncertainties, a new model reference adaptive control framework was recently proposed. Specifically, this framework was predicated on a settheoretic adaptive controller construction using generalized restricted potential functions, where its key feature was to keep the distance between the trajectories of an uncertain dynamical system and a given reference model to be less than a-priori, user-defined worstcase closed-loop system performance bound. The contribution of this paper is to generalize this framework to address disturbance rejection and system uncertainty suppression in the presence of actuator failures. A system-theoretical analysis is provided to show the strict closed-loop system performance guarantees of the proposed architecture to effectively handle actuator failures and its efficacy is demonstrated in an illustrative numerical example.