AI applications powered by deep learning models are increasingly run natively at edge. A deployed model not only encounters continuously evolving input distributions (domains) but also faces adversarial attacks from third-party. This necessitates adapting the model to shifting domains to maintain high natural accuracy, while avoiding degrading the model's robust accuracy. However, existing domain adaptation and adversarial attack preventation techniques often have conflicting optimization objectives and they rely on time-consuming training process. This paper presents RobustDA, an on-device lightweight approach that co-optimizes natural and robust accuracies in model retraining. It uses a set of low-rank adapters to retain all learned domains' knowledge with small overheads. In each model retraining, RobustDA constructs an adapter to separate domain-related and robust-related model parameters to avoid their conflicts in updating. Based on the retained knowledge, it quickly generates adversarial examples with high-quality pseudo-labels and uses them to accelerate the retraining process. We demonstrate that, comparing against 14 state-of-the-art DA techniques under 7 prevalent adversarial attacks on edge devices, the proposed co-optimization approach improves natural and robust accuracies by 6.34% and 11.41% simultaneously. Under the same accuracy, RobustDA also speeds up the retraining process by 4.09x.