Domain Adaptation (DA) techniques are important for overcoming the domain shift between the source domain used for training and the target domain where testing takes place. However, current DA methods assume that the entire target domain is available during adaptation, which may not hold in practice. This paper considers a more realistic scenario, where target data become available in smaller batches and adaptation on the entire target domain is not feasible. In our work, we introduce a new, data-constrained DA paradigm where unlabeled target samples are received in batches and adaptation is performed continually. We propose a novel source-free method for continual unsupervised domain adaptation that utilizes a buffer for selective replay of previously seen samples. In our continual DA framework, we selectively mix samples from incoming batches with data stored in a buffer using buffer management strategies and use the combination to incrementally update our model. We evaluate the classification performance of the continual DA approach with state-of-the-art DA methods based on the entire target domain. Our results on three popular DA datasets demonstrate that our method outperforms many existing state-of-the-art DA methods with access to the entire target domain during adaptation.