In many scenarios, 1) data streams are generated in real time; 2) labeled data are expensive and only limited labels are available in the beginning; 3) real-world data is not always i.i.d. and data drift over time gradually; 4) the storage of historical streams is limited and model updating can only be achieved based on a very short lookback window. This learning setting limits the applicability and availability of many Machine Learning (ML) algorithms. We generalize the learning task under such setting as a semi-supervised drifted stream learning with short lookback problem (SDSL). SDSL imposes two under-addressed challenges on existing methods in semi-supervised learning, continuous learning, and domain adaptation: 1) robust pseudo-labeling under gradual shifts and 2) anti-forgetting adaptation with short lookback. To tackle these challenges, we propose a principled and generic generation-replay framework to solve SDSL. The framework is able to accomplish: 1) robust pseudo-labeling in the generation step; 2) anti-forgetting adaption in the replay step. To achieve robust pseudo-labeling, we develop a novel pseudo-label classification model to leverage supervised knowledge of previously labeled data, unsupervised knowledge of new data, and, structure knowledge of invariant label semantics. To achieve adaptive antiforgetting model replay, we propose to view the anti-forgetting adaptation task as a flat region search problem. We propose a novel minimax game-based replay objective function to solve the flat region search problem and develop an effective optimization solver. Finally, we present extensive experiments to demonstrate our framework can effectively address the task of anti-forgetting learning in drifted streams with short lookback