Document-Level Relation Extraction aims at predicting relations between entities from multiple sentences. A common practice is to select multi-label classification thresholds to decide whether a relation exists between an entity pair. However, in the document-level task, most entity pairs do not express any relations, resulting in a highly imbalanced distribution between positive and negative classes. We argue that the imbalance problem affects threshold selection and may lead to incorrect “no-relation” predictions. In this paper, we propose to down-weight the easy negatives by utilizing a distance between the classification threshold and the predicted score of each relation. Our novel Adaptive Hinge Balance Loss measures the difficulty of each relation class with the distance, putting more focus on hard, misclassified relations, i.e. the minority positive relations. Experiment results on Re-DocRED demonstrate the superiority of our approach over other balancing methods. Source codes are available at https://github.com/Jize-W/HingeABL.