A bistable system exhibits two distinct response levels, so it may act as a switch. Bistability is a common feature of many dynamical systems, including single and interconnected neurons. In general, it provides a simple model mechanism for the gating of neural activity, which may be ubiquitously important for the operation of real nervous systems. Here we explore the range of conditions under which bistability is possible in recurrent neural networks. In particular, we explore whether oscillations affect the capacity of a circuit to produce bistable behavior. To this end, we simulate and compare three types of networks: one with homogeneous parameters (so individual units are identical), another with heterogeneous parameters, and a third that is forced to produce oscillatory activity. We use an evolutionary strategy to generate networks of each type that are bistable in the presence of noise. We find that all evolved networks reach a nearly equal capacity to sustain bistability in the presence of high noise, suggesting that such capacity is not greatly limited by other constraints that may be placed upon a network.