The rise of antibiotic-resistant bacterial infections poses a global threat. Antibiotic resistance development is generally studied in batch cultures which conceals the heterogeneity in cellular responses. Using single-cell imaging, we studied the growth response of Escherichia coli to sub-inhibitory and inhibitory concentrations of nine antibiotics. We found that the heterogeneity in growth increases more than what is expected from growth rate reduction for three out of the nine antibiotics tested. For two antibiotics (rifampicin and nitrofurantoin), we found that sub-populations were able to maintain growth at lethal antibiotic concentrations for up to 10 generations. This perseverance of growth increased the population size and led to an up to 40-fold increase in the frequency of antibiotic resistance mutations in gram-negative and gram-positive species. We conclude that antibiotic perseverance is a common phenomenon that has the potential to impact antibiotic resistance development across pathogenic bacteria.