Neural models command state-of-the-art performance across NLP tasks, including ones involving “reasoning”. Models claiming to reason about the evidence presented to them should attend to the correct parts of the input while avoiding spurious patterns therein, be self-consistent in their predictions across inputs, and be immune to biases derived from their pre-training in a nuanced, context- sensitive fashion. Do the prevalent *BERT- family of models do so? In this paper, we study this question using the problem of reasoning on tabular data. Tabular inputs are especially well-suited for the study—they admit systematic probes targeting the properties listed above. Our experiments demonstrate that a RoBERTa-based model, representative of the current state-of-the-art, fails at reasoning on the following counts: it (a) ignores relevant parts of the evidence, (b) is over- sensitive to annotation artifacts, and (c) relies on the knowledge encoded in the pre-trained language model rather than the evidence presented in its tabular inputs. Finally, through inoculation experiments, we show that fine- tuning the model on perturbed data does not help it overcome the above challenges.