In this paper, we propose a novel decentralized control method to maintain Line-of-Sight connectivity for multi-robot networks in the presence of Guassian-distributed localization uncertainty. In contrast to most existing work that assumes perfect positional information about robots or enforces overly restrictive rigid formation against uncertainty, our method enables robots to preserve Line-of-Sight connectivity with high probability under unbounded Gaussian-like positional noises while remaining minimally intrusive to the original robots' tasks. This is achieved by a motion coordination framework that jointly optimizes the set of existing Line-of-Sight edges to preserve and control revisions to the nominal task-related controllers, subject to the safety constraints and the corresponding composition of uncertainty-aware Line-of-Sight control constraints. Such compositional control constraints, expressed by our novel notion of probabilistic Line-of-Sight connectivity barrier certificates (PrLOS-CBC) for pairwise robots using control barrier functions, explicitly characterize the deterministic admissible control space for the two robots. The resulting motion ensures Line-of-Sight connectedness for the robot team with high probability. Furthermore, we propose a fully decentralized algorithm that decomposes the motion coordination framework by interleaving the composite constraint specification and solving for the resulting optimization-based controllers. The optimality of our approach is justified by the theoretical proofs. Simulation and real-world experiments results are given to demonstrate the effectiveness of our method.