It sounds counterintuitive, but see:
Science 18 November 2011, Vol. 334 no. 6058 pp. 982-986
ABSTRACT: Bacteria become highly tolerant to antibiotics when nutrients are limited. The inactivity of antibiotic targets caused by starvation-induced growth arrest is thought to be a key mechanism producing tolerance. Here we show that the antibiotic tolerance of nutrient-limited and biofilm Pseudomonas aeruginosa is mediated by active responses to starvation, rather than by the passive effects of growth arrest. The protective mechanism is controlled by the starvation-signaling stringent response (SR), and our experiments link SR-mediated tolerance to reduced levels of oxidant stress in bacterial cells. Furthermore, inactivating this protective mechanism sensitized biofilms by several orders of magnitude to four different classes of antibiotics and markedly enhanced the efficacy of antibiotic treatment in experimental infections.
See also: Antibiotic resistance is ancient.