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White blood cell (WBC) classification plays a vital role in hematology for diagnosing various medical conditions. However, it faces significant challenges due to domain shifts caused by variations in sample sources (e.g., blood or bone marrow) and differing imaging conditions across hospitals. Traditional deep learning models often suffer from catastrophic forgetting in such dynamic environments, while foundation models, though generally robust, experience performance degradation when the distribution of inference data differs from that of the training data. To address these challenges, we propose a generative replay-based Continual Learning (CL) strategy designed to prevent forgetting in foundation models for WBC classification. Our method employs lightweight generators to mimic past data with a synthetic latent representation to enable privacy-preserving replay. To showcase the effectiveness, we carry out extensive experiments with a total of four datasets with different task ordering and four backbone models including ResNet50, RetCCL, CTransPath, and UNI. Experimental results demonstrate that conventional fine-tuning methods degrade performance on previously learned tasks and struggle with domain shifts. In contrast, our continual learning strategy effectively mitigates catastrophic forgetting, preserving model performance across varying domains. This work presents a practical solution for maintaining reliable WBC classification in real-world clinical settings, where data distributions frequently evolve.