Fractional killing in response to drugs is a hallmark of nongenetic cellular heterogeneity. Yet how
individual lineages evade drug treatment, as observed in bacteria and cancer cells, is not quantitatively
understood. We study a stochastic population model with age-dependent division and death rates, allowing
for persistence. In periodic drug environments, we discover peaks in the survival probabilities at division or
death times that are multiples of the environment duration. The survival resonances are unseen in
unstructured populations and are amplified by persistence.