  We consider losses in collisions of ultracold molecules described by a simple
statistical short-range model that explicitly accounts for the limited lifetime
of classically chaotic collision complexes. This confirms that thermally
sampling many isolated resonances leads to a loss cross section equal to the
elastic cross section derived by Mayle et al. [Phys. Rev. A 85, 062712 (2012)],
and this makes precise the conditions under which this is the case.
Surprisingly, we find that the loss is nonuniversal. We also consider the case
that loss broadens the short-range resonances to the point that they become
overlapping. The overlapping resonances can be treated statistically even if
the resonances are sparse compared to $k_BT$, which may be the case for many
molecules. The overlap results in Ericson fluctuations which yield a
nonuniversal short-range boundary condition that is independent of energy over
a range much wider than is sampled thermally. Deviations of experimental loss
rates from the present theory beyond statistical fluctuations and the
dependence on a background phase shift are interpreted as non-chaotic dynamics
of short-range collision complexes.
