In the idling brain, neuronal circuits often exhibit transitions between periods of sustained firing (UP state) and quiescence (DOWN state). Although these dynamics occur across multiple areas and behavioral conditions, the underlying mechanisms remain unclear. Here we analyze spontaneous population activity from the somatosensory cortex of urethane-anesthetized rats. We find that UP and DOWN periods are variable (i.e. non-rhythmic) and that the population rate shows no significant decay during UP periods. We build a network model of excitatory (E) and inhibitory (I) neurons that exhibits a new bistability between a quiescent state and a balanced state of arbitrarily low rate. Fluctuating inputs trigger state transitions. Adaptation in E cells paradoxically causes a marginal decay of E-rate but a marked decay of I-rate, a signature of balanced bistability that we validate experimentally. Our findings provide evidence of a bistable balanced network that exhibits non-rhythmic state transitions when the brain rests.