Deep learning models have demonstrated exceptional performance in a variety of real-world applications. These successes are often attributed to strong base models that can generalize to novel tasks with limited supporting data while keeping prior knowledge intact. However, these impressive results are based on the availability of a large amount of high-quality data, which is often lacking in specialized biomedical applications. In such fields, models are often developed with limited data that arrive incrementally with novel categories. This requires the model to adapt to new information while preserving existing knowledge. Few-Shot Class-Incremental Learning (FSCIL) methods offer a promising approach to addressing these challenges, but they also depend on strong base models that face the same aforementioned limitations. To overcome these constraints, we propose AnchorInv following the straightforward and efficient buffer-replay strategy. Instead of selecting and storing raw data, AnchorInv generates synthetic samples guided by anchor points in the feature space. This approach protects privacy and regularizes the model for adaptation. When evaluated on three public physiological time series datasets, AnchorInv exhibits efficient knowledge forgetting prevention and improved adaptation to novel classes, surpassing state-of-the-art baselines.