We study the temperature dependence of the lifetime of geometric and geometric/energetic water hydrogen-bonds (H-bonds), down to supercooled water, through molecular dynamics. The probability and lifetime of H-bonds that break either by translational or librational motions and those of energetic broken H-bonds, along with the effects of transient broken H-bonds and transient H-bonds, are considered. We show that the fraction of transiently broken energetic H-bonds increases at low temperatures and that this energetic breakdown is caused by oxygen-oxygen electrostatic repulsions upon too small amplitude librations to disrupt geometric H-bonds. Hence, differences between geometric and energetic continuous H-bond lifetimes are associated with large H-bond energy fluctuations, in opposition to moderate geometric fluctuations, within common energetic and geometric H-bond definition thresholds. Exclusion of transient broken H-bonds and transient H-bonds leads to H-bond definition-independent mean lifetimes and activation energies, ~11 kJ/mol, consistent with the reactive flux method and experimental scattering results. Further, we show that power law decay of specific temporal H-bond lifetime probability distributions is associated with librational and translational motions that occur on the time scale (~0.1 ps) of H-bond breaking /re-forming dynamics. While our analysis is diffusion-free, the effect of diffusion on H-bond probability distributions where H-bonds are allowed to break and re-form, switching acceptors in between, is shown to result in neither exponential nor power law decay, similar to the reactive flux correlation function.