The Epoch of Reionization (EoR) features a rich interplay between the first luminous sources and the low-density gas of the intergalactic medium (IGM), where photons from these sources ionize the IGM. There are currently few observational constraints on key observables related to the EoR, such as the midpoint and duration of reionization. Although upcoming observations of the 21 cm power spectrum with next-generation radio interferometers such as the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA) are expected to provide information about the midpoint of reionization readily, extracting the duration from the power spectrum alone is a more difficult proposition. As an alternative method for extracting information about reionization, we present an application of convolutional neural networks (CNNs) to images of reionization. These images are two-dimensional in the plane of the sky, and extracted at a series of redshift values to generate image cubes that are qualitatively similar to those of the HERA and the SKA will generate in the near future. Additionally, we include the impact that the bright foreground signal from the the Milky Way imparts on such image cubes from interferometers, but do not include the noise induced from observations. We show that we are able to recover the duration of reionization $Delta$z to within 5% using CNNs, assuming that the midpoint of reionization is already relatively well constrained. These results have exciting impacts for estimating $tau$, the optical depth to the cosmic microwave background, which can help constrain other cosmological parameters.