The integration of simple robots into real-world scenarios necessitates their capacity to collaborate within small groups while effectively managing system faults. In this work we introduce the problem of robust matching maximization, in which a group of simple distributed decision-making robots should match in pairs, despite the activity of faulty robots within the group. These faulty robots, indistinguishable and prone to disruptive behavior, may prevent the nonfaulty robots from successfully meeting. We therefore devise distributed algorithms aiming at maximizing the number of pairs assembled by the nonfaulty robots. By establishing both lower and upper bounds on the achievable pairings, we explore the algorithms theoretically, and offer a rigorous empirical analysis, testing their robustness to various types of failures, robot characteristics, and fault intensity.