The analysis of fading channels is often done under the assumption that the additive noise is white and Gaussian, and that the receiver has precise knowledge of the realization of the fading process. These assumptions imply the optimality of Gaussian codebooks and of a modified nearest-neighbor decoding rule. Here we study the robustness of this communication scheme with respect to errors in the estimation of the fading process. We quantify the degradation in performance that results from estimation errors, and demonstrate the lack of robustness of this scheme. We treat the "flat fading" case exclusively.