We address distributed estimation of the state of a linear plant by a set of agents. The problem is cast in a setting where the communication capabilities of an agent might be deactivated from time to time, due to failures in the communication devices or malicious attacks. An observer architecture is proposed to achieve our estimation goal, based on a multi-hop subspace decomposition, which allows each agent to identify its observable and unobservable subspaces and asymptotically estimate the plant state by using its own measurement and the information exchanged with the neighboring agents. Uniform exponential convergence to zero of the estimation errors is proven in the presence of communication failures, under a persistence of excitation assumption. Finally, the observer performance is evaluated in simulation, showing the merits of the proposed method and suggesting directions for future developments.