Providing a mechanically stable and electronically efficient coupling between a molecule and an electrode is critical to the study of charge transfer and conductance of the molecule. A common method is to link the molecule to Au electrodes via a linker (e.g., thiol terminal of the molecule). Here we study the mechanical stability and electronic coupling of a S-Au bond in single-molecule junctions over a broad range of electrode potentials. Our results show that the mechanical and electromechanical properties of molecule-electrode contact undergo a systematic change with the potential involving Au oxidation at positive potentials and S protonation at negative potentials. The study establishes the potential range for a stable S-Au bond and determines the potential dependence of the mechanical and electromechanical properties of the molecule-electrode contact, which is crucial to the interpretation of potential-dependent charge transfer in electrochemistry and electrochemical gating of charge transport in molecular electronics.