The present Letter reports a quantitative analysis of contact mechanics in metal-molecule-metal junctions at a single atom/molecule level through investigating their lifetime at cryogenic temperature. We elucidated that the force breaking mechanism of atomic/molecular junctions is stretching speed dependent, attributed to suppression of contact structure relaxation processes at high strain rate conditions. We also provide solid evidence that strain exerted in the preformation stage of molecular junctions poses extra strain energy that accelerates their eventual fracture. Nonetheless, we find that single-molecule junctions subjected to mechanical stretching at 0.6 pm/s can be held for approximately 100 s on average at 77 K and for a much prolonged period when freezing the elongation after forming the molecular junctions by virtue of moderate thermal destabilizations, the fluctuation-free condition of which provides optimal experimental platform for performing reliable measurements of single molecule electron transport properties.