  We study the spontaneous dissociation of diatomic molecules produced in cold
atomic gases via magnetically tunable Feshbach resonances. We provide a
universal formula for the lifetime of these molecules that relates their decay
to the scattering length and the loss rate constant for inelastic spin
relaxation. Our universal treatment as well as our exact coupled channels
calculations for $^{85}$Rb dimers predict a suppression of the decay over
several orders of magnitude when the scattering length is increased. Our
predictions are in good agreement with recent measurements of the lifetime of
$^{85}$Rb$_2$.
