The energy relaxation times of the fundamental stretching modes in the electronic ground state of OH-, OD-, SH-, and TeH- in a variety of alkali halides are measured by incoherent laser saturation and found to vary from 0.3 to 3 ns at 1.7 K. These vibrational lifetimes are between 4 and 8 orders of magnitude smaller than those of other heteronuclear diatomics diluted in crystals, including the ionic systems of CN- in salts and the neutral deuterides, DCl and ND, and oxides, CO and NO, in rare-gas matrices. Unlike these other systems, the chalcogen-hydride-doped alkali halides have a librational mode at frequencies well above the top of the host phonon band. This makes the librational decay channel a lower order process than relaxation into phonons. An energy gap law can be fit to the data, in which the relaxation times vary exponentially with the number of accepting reorientational modes. This model can explain the fact that OH- and OD- in KCl have nearly the same lifetimes, since the vibrational and librational frequencies both have the same isotope shift. Furthermore, previous persistent spectral hole burning measurements of SH- in mixed crystals are consistent with a picture in which the defects reorient during vibrational de-excitation. It is found that the reorientational decay rates are much faster than the equal-decay-order relaxation of CN- into translational modes in the silver and sodium halides. This could be explained by a factor of similar to 3 enhancement in the vibrational coupling constant to reorientations as compared to translations, but the relative strengths of the appropriate sidebands do not appear to support such an enhancement. The relaxation times of the diatomic hydrides are also found to be much smaller in ionic than in van der Waals hosts, even for equal order reorientational relaxation, suggesting that Coulombic forces significantly increase the V-R coupling strength.