Recent successes in deep learning have started to impact neuroscience. Of particular significance are claims that current segmentation algorithms achieve "super-human" accuracy in an area known as connectomics. However, as we will show, these algorithms do not effectively generalize beyond the particular source and brain tissues used for training -- severely limiting their usability by the broader neuroscience community. To fill this gap, we describe a novel connectomics challenge for source- and tissue-agnostic reconstruction of neurons (STARN), which favors broad generalization over fitting specific datasets. We first demonstrate that current state-of-the-art approaches to neuron segmentation perform poorly on the challenge. We further describe a novel convolutional recurrent neural network module that combines short-range horizontal connections within a processing stage and long-range top-down connections between stages. The resulting architecture establishes the state of the art on the STARN challenge -- improving the prospect for computer vision to allow for widespread fully-automated connectomics analysis. Here, we address the poor generalization of computer vision systems in connectomics with a novel challenge: the source- and tissue-agnostic reconstruction of neurons. This challenge presents a "training" dataset consisting of five publicly available and annotated tissue volumes representing a variety of organisms and imaging configurations (CREMI, FIB-25, and SNEMI3D); evaluation is performed on an independent volume [1] annotated by our group. We will demonstrate that the STARN challenge defeats state-of-the-art systems for neuron reconstruction.