Federated learning (FL) is a promising approach for edge/IoT-based distributed machine learning, where both privacy and bandwidth efficiency are essential. However, as time progresses, edge/IoT-based FL faces challenges such as unpredictable concept drift, leading to model performance degradation and the need for frequent retraining. To address these challenges, we propose a federated learning framework designed for heterogeneous IoT devices, capable of handling continuous data distribution changes while accounting for limited storage resources. Our framework introduces a server-side drift detection method to minimize bandwidth usage and optimize retraining times, conserving IoT device resources. We also present an efficient storage management strategy to mitigate catastrophic forgetting by selectively managing incoming data streams within device constraints. Additionally, we develop an exemplar-based online continual learning algorithm that leverages class prototypes in the deep feature space to further combat catastrophic forgetting. We evaluate our framework on image classification tasks using ImageNet and CIFAR-100 datasets across four model architectures, demonstrating significant improvements in adaptation to concept drift and long-term performance stability compared to baseline FL approaches.