The fundamental obstacle is catastrophic forgetting: training on new data overwrites the weights that encoded old knowledge. Humans don't have this problem (learning French doesn't make you forget English) because biological neural networks use different mechanisms for memory consolidation. Artificial neural networks store all knowledge in shared weights, making any update a potential disruption to existing capabilities.
Several strategies partially address continual learning: replay methods (mix old data with new data during training), regularization methods (penalize changes to weights important for old tasks, like EWC), architecture methods (allocate different parameters to different tasks), and retrieval-augmented approaches (store knowledge externally in a database rather than in weights). None fully solve the problem, but each enables some degree of incremental learning.
In practice, RAG (Retrieval-Augmented Generation) serves as a pragmatic substitute for true continual learning. Instead of updating the model's weights with new information, you update an external knowledge base that the model consults at inference time. This sidesteps catastrophic forgetting entirely but has limitations: the model's reasoning capabilities don't improve, only its access to information. True continual learning would improve both knowledge and capabilities simultaneously.