This paper studies the mean-square stability of heterogeneous LTI vehicular platoons with inter-vehicle communication channels affected by random data loss. We consider a discrete-time platoon system with predecessor following topology and a constant time-headway spacing policy. Lossy channels are modeled by Bernoulli processes and allowed to be correlated in space. We make use of a class of compensation strategies to reduce the effect of data loss. Necessary and sufficient conditions are derived to guarantee the convergence of the mean and variance of the tracking errors, which depend not only on the controller design but also on the compensation strategy and the probabilities of successful transmission. We illustrate the theoretical results through numerical simulations, describing different platoon behaviors. We also provide insights on the mean-square stability as a necessary condition for string stability in this stochastic setting.