In this paper we address the question of robustness of critical bit rates for the stabilization of networked control systems over digital communication channels. For a deterministic nonlinear system, the smallest bit rate above which practical stabilization (in the sense of set-invariance) can be achieved is measured by the invariance entropy. Under the assumptions of chain controllability and uniform hyperbolicity on the set of interest, we prove that the invariance entropy varies continuously with respect to system parameters. Hence, in this case the critical bit rate is robust with respect to small perturbations. (C) 2018 Elsevier Ltd. All rights reserved.