Many computer vision applications, including image classification, matching, and retrieval use global image representations, such as the Fisher vector, to encode a set of local image patches. To describe these patches, many local descriptors have been designed to be robust against lighting changes and noise. However, local image descriptors are unstable when the underlying image signal is low. Such low-signal patches are sensitive to small image perturbations, which might come e.g., from camera noise or lighting effects. In this paper, we first quantify the relation between the signal strength of a patch and the instability of that patch, and second, we extend the standard Fisher vector framework to explicitly take the descriptor instabilities into account. In comparison to common approaches to dealing with descriptor instabilities, our results show that modeling local descriptor instability is beneficial for object matching, image retrieval, and classification.