Robot navigation requires an autonomy pipeline that is robust to environmental changes and effective in varying conditions. Teach and Repeat (T&R) navigation has shown high performance in autonomous repeated tasks under challenging circumstances, but research within T&R has predominantly focused on motion planning as opposed to motion control. In this paper, we propose a novel T&R system based on a robust motion control technique for a skid-steering mobile robot using sliding-mode control that effectively handles uncertainties that are particularly pronounced in the T&R task, where sensor noises, parametric uncertainties, and wheel-terrain interaction are common challenges. We first theoretically demonstrate that the proposed T&R system is globally stable and robust while considering the uncertainties of the closed-loop system. When deployed on a Clearpath Jackal robot, we then show the global stability of the proposed system in both indoor and outdoor environments covering different terrains, outperforming previous state-of-the-art methods in terms of mean average trajectory error and stability in these challenging environments. This paper makes an important step towards long-term autonomous T&R navigation with ensured safety guarantees.