Deep Learning for medical imaging faces challenges in adapting and generalizing to new contexts. Additionally, it often lacks sufficient labeled data for specific tasks requiring significant annotation effort. Continual Learning (CL) tackles adaptability and generalizability by enabling lifelong learning from a data stream while mitigating forgetting of previously learned knowledge. Active Learning (AL) reduces the number of required annotations for effective training. This work explores both approaches (CAL) to develop a novel framework for robust medical image analysis. Based on the automatic recognition of shifts in image characteristics, Replay-Base Architecture for Context Adaptation (RBACA) employs a CL rehearsal method to continually learn from diverse contexts, and an AL component to select the most informative instances for annotation. A novel approach to evaluate CAL methods is established using a defined metric denominated IL-Score, which allows for the simultaneous assessment of transfer learning, forgetting, and final model performance. We show that RBACA works in domain and class-incremental learning scenarios, by assessing its IL-Score on the segmentation and diagnosis of cardiac images. The results show that RBACA outperforms a baseline framework without CAL, and a state-of-the-art CAL method across various memory sizes and annotation budgets. Our code is available in https://github.com/RuiDaniel/RBACA .