Recognition of an artistic style of a painting is a complex task that requires significant knowledge and expertise. This paper is a continuation of our previous studies aiming to develop an automatic style classification method. While our previous research was limited to the analysis of paintings with no visible damages, this study investigates the effect of partial damage to a painting on the accuracy of the automatic style recognition. A two-stage approach was adapted with images being first classified patch by patch by a convolutional neural network (CNN) and then by a shallow neural network (NN) trained to make the final decision based on the outcomes achieved by individual patches (image subregions). The partial damage was simulated by superimposing randomly positioned circles with randomized pixel values. It was found that the combination of damaged and nondamaged painting in the training dataset and the strengthening role of the final decision-making classifier increase the system's robustness to partial damages, while at the same time maintaining a relatively high classification accuracy of non-damaged artworks.