Cortical neuron spiking activity is broadly classified as temporally irregular and asynchronous. Model networks with a balance between large recurrent excitation and inhibition capture these two features, and are a popular framework relating circuit structure and network dynamics, though are traditionally restricted to a single attractor. We analyze paired whole cell voltage-clamp recordings from spontaneously active neurons in mouse auditory cortex slices (Graupner & Reyes, 2013) showing a network where correlated excitation and inhibition effectively cancel, except for intermittent periods when the network shows a macroscopic synchronous event. These data suggest that while the core mechanics of balanced activity are important, we require new theories capturing these brief but powerful periods when balance fails. Recent work by Mongillo et.al. (2012) showed that balanced networks with short-term synaptic plasticity can depart from strict linear dynamics. We extend this model by incorporating finite network size, introducing strong nonlinearities in the firing rate dynamics and allowing finite size induced noise to elicit large scale, yet infrequent, synchronous events. We identify core requirements for system size and network plasticity to capture the transient synchronous activity observed in our experimental data set. Our model properly mediates between the asynchrony of balanced activity and the tendency for strong recurrence to promote macroscopic population dynamics.