Recent advances in graphene and other two-dimensional (2D) material synthesis and characterization have led to their use in emerging technologies, including flexible electronics. However, a major challenge is electrical contact stability, especially under mechanical straining or dynamic loading, which can be important for 2D material use in microelectromechanical systems. In this letter, we investigate the stability of dynamic electrical contacts at a graphene/metal interface using atomic force microscopy (AFM), under static conditions with variable normal loads and under sliding conditions with variable speeds. Our results demonstrate that contact resistance depends on the nature of the graphene support, specifically whether the graphene is free-standing or supported by a substrate, as well as on the contact load and sliding velocity. The results of the dynamic AFM experiments are corroborated by simulations, which show that the presence of a stiff substrate, increased load, and reduced sliding velocity lead to a more stable low-resistance contact.