Continual Learning (CL) in Automatic Speech Recognition (ASR) suffers from catastrophic forgetting when adapting to new tasks, domains, or speakers. A common strategy to mitigate this is to store a subset of past data in memory for rehearsal. However, rehearsal-based methods face key limitations: storing data is often costly, infeasible with pre-trained models, or restricted by privacy regulations. Running existing rehearsal-based methods with smaller memory sizes to alleviate these issues usually leads to degraded performance. We propose a rehearsal-based CL method that remains effective even with minimal memory. It operates in two stages: first, fine-tuning on the new task; second, applying Singular Value Decomposition (SVD) to the changes in linear layers and, in a parameter-efficient manner, retraining only gating vectors on the singular values, which control to extent to which updates from the first stage are accepted, using rehearsal. We extensively test and analyze our method on two monolingual and two multilingual benchmarks. Our method reduces forgetting and outperforms state-of-the-art CL approaches for ASR, even when limited to a single utterance per previous task.