This paper studies a robust connectivity preserving rendezvous problem for a leader-following multi-robot system. Only a small group of mobile robots are informed to have access to the leader's information. A distributed control law is proposed such that connectivity preserving rendezvous is achieved regardless of the unknown nonlinear dynamics and disturbances. Although the multi-robot network has a dynamic network topology, the developed controller is able to maintain the connectivity of an initially connected communication network. Using the tools from algebraic graph theory, Lyapunov method, and nonsmooth analysis, sufficient conditions on the convergence of the closed-loop error systems are derived.