The application of deep learning to automatic speech recognition (ASR) has yielded dramatic accuracy increases for languages with abundant training data, but languages with limited training resources have yet to see accuracy improvements on this scale. In this paper, we compare a fully convolutional approach for acoustic modelling in ASR with a variety of established acoustic modeling approaches. We evaluate our method on Seneca, a low-resource endangered language spoken in North America. Our method yields word error rates up to 40% lower than those reported using both standard GMM-HMM approaches and established deep neural methods, with a substantial reduction in training time. These results show particular promise for languages like Seneca that are both endangered and lack extensive documentation.