Deep autoencoder (DAE) frameworks have demonstrated their effectiveness in reducing channel state information (CSI) feedback overhead in massive multiple-input multiple-output (mMIMO) orthogonal frequency division multiplexing (OFDM) systems. However, existing CSI feedback models struggle to adapt to dynamic environments caused by user mobility, requiring retraining when encountering new CSI distributions. Moreover, returning to previously encountered environments often leads to performance degradation due to catastrophic forgetting. Continual learning involves enabling models to incorporate new information while maintaining performance on previously learned tasks. To address these challenges, we propose a generative adversarial network (GAN)-based learning approach for CSI feedback. By using a GAN generator as a memory unit, our method preserves knowledge from past environments and ensures consistently high performance across diverse scenarios without forgetting. Simulation results show that the proposed approach enhances the generalization capability of the DAE framework while maintaining low memory overhead. Furthermore, it can be seamlessly integrated with other advanced CSI feedback models, highlighting its robustness and adaptability.