Within clinical practise, a shift in the distribution of data collected over time is commonly observed. This occurs generally due to deliberate changes in acquisition hardware but also through natural, unforeseen shifts in the hardware’s physical properties like scanner SNR and gradient non-linearities. These domain shifts thus may not be known a-priori, but may cause significant degradation in the diagnostic performance of machine learning models. A deployed diagnostic system must therefore be robust to such unpredictable and continuous domain shifts. However, given the infrastructure and resource constraints pervasive in clinical settings in developing countries, such robustness must be achieved under finite memory and data privacy constraints. In this work, we propose a domain-incremental learning approach that leverages vector quantization to efficiently store and replay hidden representations under limited memory constraints. Our proposed approach validated on well known large-scale public Chest X-ray datasets achieves significant reduction in catastrophic forgetting over previous approaches in medical imaging, while requiring no prior knowledge of domain shift boundaries and a constrained memory. Finally, we also formulate a more natural continual learning setting for medical imaging using a tapered uniform distribution schedule with gradual interleaved domain shifts.