Antibiotic tolerance, or the ability of bacteria to survive antibiotic treatment in the absence of genetic resistance, has been linked to chronic and recurrent infections. Tolerant cells are often characterized by a low metabolic state, against which most clinically used antibiotics are ineffective. Here, we show that tolerance readily evolves against antibiotics that are strongly dependent on bacterial metabolism, but does not arise against antibiotics whose efficacy is only minimally affected by metabolic state. We identify a mechanism of tolerance evolution in E. coli involving deletion of the sodium-proton antiporter gene nhaA, which results in downregulated metabolism and upregulated stress responses. Additionally, we find that cycling of antibiotics with different metabolic dependencies interrupts evolution of tolerance in vitro, increasing the lifetime of treatment efficacy. Our work highlights the potential for limiting the occurrence and extent of tolerance by accounting for antibiotic dependencies on bacterial metabolism.