Wide adoption of artificial neural networks in various domains has led to an increasing interest in defending adversarial attacks against them. Preprocessing defense methods such as pixel discretization are particularly attractive in practice due to their simplicity, low computational overhead, and applicability to various systems. It is observed that such methods work well on simple datasets like MNIST, but break on more complicated ones like ImageNet under recently proposed strong white-box attacks. To understand the conditions for success and potentials for improvement, we study the pixel discretization defense method, including more sophisticated variants that take into account the properties of the dataset being discretized. Our results again show poor resistance against the strong attacks. We analyze our results in a theoretical framework and offer strong evidence that pixel discretization is unlikely to work on all but the simplest of the datasets. Furthermore, our arguments present insights why some other preprocessing defenses may be insecure.