Most existing deep learning models for remote sensing scene classification (RSSC) adopt an offline learning paradigm, where all classes are jointly optimized on fixed-class datasets. In dynamic real-world scenarios with streaming data and emerging classes, such paradigms are inherently prone to catastrophic forgetting when models are incrementally trained on new data. Recently, a growing number of class-incremental learning (CIL) methods have been proposed to tackle these issues, some of which achieve promising performance by rehearsing training data from previous tasks. However, implementing such strategy in real-world scenarios is often challenging, as the requirement to store historical data frequently conflicts with strict memory constraints and data privacy protocols. To address these challenges, we propose a novel memory-efficient feature-replay CIL framework (FR-CIL) for RSSC that retains compact feature embeddings, rather than raw images, as exemplars for previously learned classes. Specifically, a progressive multi-scale feature enhancement (PMFE) module is proposed to alleviate representation ambiguity. It adopts a progressive construction scheme to enable fine-grained and interactive feature enhancement, thereby improving the model’s representation capability for remote sensing scenes. Then, a specialized feature calibration network (FCN) is trained in a transductive learning paradigm with manifold consistency regularization to adapt stored feature descriptors to the updated feature space, thereby effectively compensating for feature space drift and enabling a unified classifier. Following feature calibration, a bias rectification (BR) strategy is employed to mitigate prediction bias by exclusively optimizing the classifier on a balanced exemplar set. As a result, this memory-efficient CIL framework not only addresses data privacy concerns but also mitigates representation drift and classifier bias. Extensive experiments on public datasets demonstrate the effectiveness and robustness of the proposed method. Notably, FR-CIL outperforms the leading state-of-the-art CIL methods in mean accuracy by margins of 3.75%, 3.09%, and 2.82% on the six-task AID, seven-task RSI-CB256, and nine-task NWPU-45 datasets, respectively. At the same time, it reduces memory storage requirements by over 94.7%, highlighting its strong potential for real-world RSSC applications under strict memory constraints.