Practical realization of any electronic device requires a quantitative measure of their durability for the sake of guaranteeing the reliability. Unfortunately, however, there exists no such tool for molecular devices. The present article provides a solution to this issue in molecular electronics by reporting an experimental demonstration of a quantitative comparison of thermodynamic stability of single-molecule junctions consisting of two distinct anchor groups: thiol and amine. We report solid evidence that Au-thiol bonds are far more stable than Au-amine linkages through exhibiting 2-fold longer natural lifetime of Au-aminobenzenethiol-Au single-molecule junctions compared to the Au-benzenediamine-Au counterpart. We also find that a single-molecule device composed of Au-thiol links is a factor of 100000 more stable than that configured with Au-amine contacts.