Vehicle-to-vehicle (V2V) communication is a key component of the future autonomous driving systems. V2V can provide an improved awareness of the surrounding environment, and the knowledge about the future actions of nearby vehicles. However, V2V communication is subject to different kind of failures and delays, so a distributed fault-tolerant approach is required for safe and efficient transportation. This work considers fully autonomous vehicles that operates using local sensory information, and aided with fault-tolerant V2V communication. The sensors provide all basic functionality, but are overridden by V2V whenever is possible to increase the efficiency. As an example scenario, we consider intersection crossing (IC) with autonomous vehicles that cooperate via V2V communication, and propose a fully distributed and a fault-tolerant algorithm for this problem. According to our numerical results, based on a real data set, we show the crossing delay is only slightly increased in the presence of a burst of V2V failures, and that V2V can be successfully used in most scenarios.