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.
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