Stochastic dynamics simulations of vibrational relaxation rates are reported for a carbon monoxide molecule adsorbed on the (100) face of copper. A recently developed ''molecular dynamics with electronic friction'' scheme that self-consistently incorporates both phonon and nonadiabatic electron-hole (e-h) pair mechanisms of energy dissipation is employed. Lifetimes of the C-O stretch, the CO-surface stretch, the frustrated rotation, and the frustrated in-plane translation are examined as a function of temperature between 0 and 450 K. e-h pair dissipation plays a significant role for all modes above 150 K. For the C-O internal stretching mode, the e-h pair mechanism dominates and the lifetime depends weakly on temperature. The frustrated rotational (bending) mode is calculated to have the shortest lifetime at all temperatures, and the temperature dependence is weak. The e-h pair contribution is again largest although the phonon contribution is significant. The CO-surface stretch and the frustrated in-plane translation are the longest lived modes, but exhibit a dramatic decrease in lifetime with increasing temperature. The results suggest that e-h pair dissipation plays a significant role in adsorbate dynamics at metal surfaces when there are chemisorption interactions.