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Can we distinguish between two wireless transmitters sending exactly the same message, using the same protocol? The opportunity for doing so arises due to subtle nonlinear variations across transmitters, even those made by the same manufacturer. Since these effects are difficult to model explicitly, we investigate learning device fingerprints using complex-valued deep neural networks (DNNs) that take as input the complex baseband signal at the receiver. We ask whether such fingerprints can be made robust to distribution shifts across time and locations due to clock drift and variations in the wireless channel. In this paper, we point out that, unless proactively discouraged from doing so, DNNs learn these strong confounding features rather than the nonlinear device-specific characteristics that we seek to learn. We propose and evaluate strategies, based on augmentation and estimation, to promote generalization across realizations of these confounding factors, using data from WiFi and ADS-B protocols. We conclude that, while DNN training has the advantage of not requiring explicit signal models, significant modeling insights are required to focus the learning on the effects we wish to capture.