This paper addresses a robust variant of the Ring Star Problem where we assume that at most one hub can fail, among a given subset of nodes of the network. The network should remain functional despite this failure, which means there is an edge connecting the neighbors of any hub that can fail, and every terminal is connected to two different hubs that can fail or a single hub that cannot fail. The objective is to minimize the cost of such a robust Ring Star Network structure. The problem is addressed through an integer linear programming formulation, and a Benders decomposition is proposed as an alternative solution method. Computational experiments are carried out to compare these two approaches, and the results are analyzed.