Deep learning models achieved high accuracy in pneumonia detection from chest X-rays. However, their generalization across clinical domains remains limited due to variations in imaging devices, acquisition protocols, and institutional conditions. This study introduces a replay-based domain-incremental continual learning designed to enable continual adaptation to cross-domain variations without catastrophic forgetting. The proposed method incorporates a class-aware balanced replay to maintain balanced class representation within a constrained memory and a class-aware loss to dynamically reweight class imbalance during training. Experiments conducted on a domain-shifted PneumoniaMNIST dataset consisting of five simulated domains demonstrate that the proposed method achieves an average accuracy of 88.66%, outperforming Experience Replay, Fine-Tuning, and Joint Training baselines. These findings highlight the efficacy of the proposed approach in achieving robust and consistent pneumonia detection across clinical environment variations.