The state-of-the-art abusive language detection models report great in-corpus performance, but underperform when evaluated on abusive comments that differ from the training scenario. As human annotation involves substantial time and effort, models that can adapt to newly collected comments can prove to be useful. In this paper, we investigate the effectiveness of several Unsupervised Domain Adaptation (UDA) approaches for the task of cross-corpora abusive language detection. In comparison, we adapt a variant of the BERT model, trained on large-scale abusive comments, using Masked Language Model (MLM) fine-tuning. Our evaluation shows that the UDA approaches result in sub-optimal performance, while the MLM fine-tuning does better in the cross-corpora setting. Detailed analysis reveals the limitations of the UDA approaches and emphasizes the need to build efficient adaptation methods for this task.