Concept drift and adversarial evasion are two major challenges for deploying machine learning-based malware detectors. While both have been studied separately, their combination, the adversarial robustness of drift-adaptive detectors, remains unexplored. We address this problem with AdvDA, a recent malware detector that uses adversarial domain adaptation to align a labeled source domain with a target domain with limited labels. The distribution shift between domains poses a unique challenge: robustness learned on the source may not transfer to the target, and existing defenses assume a fixed distribution. To address this, we propose a universal robustification framework that fine-tunes a pretrained AdvDA model on adversarially transformed inputs, agnostic to the attack type and choice of transformations. We instantiate it with five defense variants spanning two threat models: white-box PGD attacks in the feature space and black-box MalGuise attacks that modify malware binaries via functionality-preserving control-flow mutations. Across nine defense configurations, five monthly adaptation windows on Windows malware, and three false-positive-rate operating points, we find the undefended AdvDA completely vulnerable to PGD (100% attack success) and moderately to MalGuise (13%). Our framework reduces these rates to as low as 3.2% and 5.1%, respectively, but the optimal strategy differs: source adversarial training is essential for PGD defenses yet counterproductive for MalGuise defenses, where target-only training suffices. Furthermore, robustness does not transfer across these two threat models. We provide deployment recommendations that balance robustness, detection accuracy, and computational cost.