Control of a platoon of connected vehicles with nonlinear longitudinal dynamics subject to failure in receiving communicated and radio data is addressed in this paper. We consider a scenario when due to malfunction of communication and radio devices, required data for cooperative adaptive cruise control may be stochastically unavailable. We develop a control scheme such that under certain conditions, the regulation of the intervehicle distances in desired values can be guaranteed. Specifically, we rigorously show that if the probability of receiving the required data for each vehicle is not zero, then under the proposed control strategy, the intervehicle distances almost surely converge to the desired values. Accurate performance of radars is a key assumption in the existing results in the literature on cooperative adaptive cruise control. Hence, the main contribution of this paper is that under the proposed control strategy, the robustness of the platoon against stochastic data loss in both communication network and vehicles radars is guaranteed. Simulation results verify the acceptable performance of the proposed control strategy.