Test-time adaptation (TTA) has emerged as a promising approach to dealing with latent distribution shifts between training and testing data. However, most of existing TTA methods often struggle with small input batches, as they heavily rely on batch statistics that become less reliable as batch size decreases. In this paper, we introduce memory-based batch normalization (MemBN) to enhance the robustness of TTA across a wide range of batch sizes. MemBN leverages statistics memory queues within each batch normalization layer, accumulating the latest test batch statistics. Through dedicated memory management and aggregation algorithms, it enables to estimate reliable statistics that well represent the data distribution of the test domain in hand, leading to improved performance and robust test-time adaptation. Extensive experiments under a large variety of TTA scenarios demonstrate MemBN's superiority in terms of both accuracy and robustness.