The technical note considers a network of agents with double-integrator internal dynamics. They share information on their position states according to an arbitrary topology. For such a system, the design of a fault-tolerant decentralized regulator is addressed. The goal consists in placing the dominant poles close to prespecified locations, even in the presence of faults of the transmitting and receiving apparatuses. By combining some previous results on fault-tolerant control with singular perturbation theory, a necessary and sufficient condition for the problem to admit a solution is proved. Further, explicit formulas are given for the local regulators, which turn out to be of the first, actually minimal, order.