The perceptual salience of a sound depends on the acoustic context in which it appears. Single-neuron correlates of this contextual sensitivity can be estimated from neuronal responses to complex sounds using the nonlinear-linear "context model". Context models provide estimates of both the principal (spectrotemporal) receptive field of a neuron and a "contextual gain field" describing its nonlinear sensitivity to combinations of sound input. Previous studies of contextual gain fields in auditory cortex of anesthetized mice have revealed strong neuron-specific patterns of nonlinear sensitivity to sound context. However, the stability of these patterns over time, especially in awake animals, is unknown. We recorded electrophysiological activity of neurons in the auditory cortex of awake mice over many days using chronically implanted tetrode arrays, while also obtaining continuous measures of the animal's behavioral state (locomotor activity and pupil diameter), during repeated presentations of prolonged complex sounds. Waveform matching identified neurons that were recorded over multiple days. We estimated principal receptive fields and contextual gain fields for each neuron in each recording session, and quantified the stability of these fields within and across days. We also examined the dependence of context model fits on measures of behavioral state. Contextual gain fields of auditory cortical neurons in awake mice were remarkably stable across many days of recording, and comparable in stability to principal receptive fields. Interestingly, while patterns of contextual sensitivity to sound combinations were qualitatively similar to those previously observed in anesthetized mice, there were small but significant effects of changes in locomotion or pupil size on the ability of the context model to fit temporal fluctuations in the neuronal response. We conclude that contextual sensitivity is an integral and stable feature of the neural code in the awake auditory cortex, which might be modulated by behavioral state.