The stability and breakdown mechanism of a single molecule covalently bound to two Au electrodes via Au-S bonds were studied at room temperature. The distance over which a molecular junction can be stretched before breakdown was measured using a scanning tunneling microscopy break junction approach as a function of stretching rate. At low stretching rates, the stretching distance is small and independent of stretching rate. Above a certain stretching rate, it increases linearly with the logarithm of stretching rate. At very high stretching rates, the stretching distance reaches another plateau and becomes insensitive to the stretching rate again. The three regimes are well described by a thermodynamic bondbreaking model. A comparative study of Au-Au atomic point contacts indicates that the breakdown of the molecular junctions takes place at Au-Au bonds near the molecule -electrode contact. By fitting the experimental data with the model, the lifetime and binding energy were extracted. Both quantities are found to have broad distributions, owing to large variations in the molecule-electrode contact geometry. Although the molecular junctions are short-lived on average, certain contact geometries are considerably more stable. Several types of stochastic fluctuations were observed in the conductance of the molecule junctions, which are attributed to the atomic level rearrangement of the contact geometry, and bond breakdown and reformation processes. The possibility of bond reformation increases the apparent lifetime of the molecular junctions.