  Resistivities of heavy-fermion insulators typically saturate below a
characteristic temperature $T^*$. For some, metallic surface states,
potentially from a non-trivial bulk topology, are a likely source of residual
conduction. Here, we establish an alternative mechanism: At low temperature, in
addition to the charge gap, the scattering rate turns into a relevant energy
scale, invalidating the semiclassical Boltzmann picture. Finite lifetimes of
intrinsic carriers limit conduction, impose the existence of a crossover $T^*$,
and control - now on par with the gap - the quantum regime emerging below it.
We showcase the mechanism with realistic many-body simulations and elucidate
how the saturation regime of the Kondo insulator Ce$_3$Bi$_4$Pt$_3$, for which
residual conduction is a bulk property, evolves under external pressure and
varying disorder. Using a phenomenological formula we derived for the quantum
regime, we also unriddle the ill-understood bulk conductivity of SmB$_6$ -
demonstrating that our mechanism is widely applicable to correlated narrow-gap
semiconductors.
