The prefrontal cortex (PFC) plays an important role in complex cognitive computations, including planning and decision making. Although recurrent spiking neural network (SNN) software models of PFC have been successful in reproducing many of its cognitive computational aspects, little attention has been devoted to the question of how such systems can perform with low-resolution parameters and be robust to noise and variability in their input signals and state variables. Here, we present a mixed-signal analog/digital neuromorphic implementation of a state-dependent SNN architecture that addresses these issues by construction. The network relies on synaptic dis-inhibition to ensure robust decision making even in the face of very large variability. Depending on its connectivity, the network can either perform robustly in a deterministic way or exploit the device mismatch and noise to explore stochastically multiple states in constraint satisfaction problems (CSPs). We validate the architecture by mapping it onto a network of spiking neurons in a multi-core mixed-signal neuromorphic system and presenting experimental results for three different examples of CSPs.