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Safe deployment of deep learning systems in critical real world applications requires models to make very few mistakes, and only under predictable circumstances. In this work, we address this problem using an abstaining classifier that is tuned to have $>$95% accuracy, and then identify the determinants of abstention using LIME. Essentially, we are training our model to learn the attributes of pathology reports that are likely to lead to incorrect classifications, albeit at the cost of reduced sensitivity. We demonstrate an abstaining classifier in a multitask setting for classifying cancer pathology reports from the NCI SEER cancer registries on six tasks of interest. For these tasks, we reduce the classification error rate by factors of 2--5 by abstaining on 25--45% of the reports. For the specific task of classifying cancer site, we are able to identify metastasis, reports involving lymph nodes, and discussion of multiple cancer sites as responsible for many of the classification mistakes, and observe that the extent and types of mistakes vary systematically with cancer site (e.g., breast, lung, and prostate). When combining across three of the tasks, our model classifies 50% of the reports with an accuracy greater than 95% for three of the six tasks\edit, and greater than 85% for all six tasks on the retained samples. Furthermore, we show that LIME provides a better determinant of classification than measures of word occurrence alone. By combining a deep abstaining classifier with feature identification using LIME, we are able to identify concepts responsible for both correctness and abstention when classifying cancer sites from pathology reports. The improvement of LIME over keyword searches is statistically significant, presumably because words are assessed in context and have been identified as a local determinant of classification.