Medical vision-language models (VLMs) such as BiomedCLIP generalize broadly, but adapting them to a clinical service is as much a safety problem as an accuracy one. Updating a deployed model for a new imaging modality can fail silently in two ways that harm patients: it can forget modalities it already handled (catastrophic forgetting), and it can drift from its trustworthy pretrained prior toward modality-specific shortcuts. We study parameter-efficient continual adaptation through these two properties rather than leaderboard accuracy, presenting CADRE: a frozen-backbone framework combining low-rank adaptation (LoRA) with an online, self-scaling, similarity-aware elastic weight consolidation term that bounds retained-competence loss, and an anchor-to-prior penalty bounding embedding drift from the frozen prior. Two short guarantees, a bound on total consolidation mass and a scale-invariance property, remove the scale-related sources of vanilla EWC's order fragility. Using breast cancer across three maximally dissimilar modalities (histopathology, ultrasound, chest radiography) as a controlled cross-modality stress test, under a multi-seed, multi-order protocol with paired significance testing and training approximately 0.23% of parameters, CADRE attains the highest accuracy, SPQ, and backward transfer and the lowest forgetting among adapting methods, reducing forgetting roughly sevenfold versus the strongest regularized baseline (0.075 to 0.011; paired p=0.023) and achieving positive backward transfer where every baseline is negative. We frame these as stability properties aligned with clinical-safety desiderata, not a deployment guarantee; robustness to distribution shift and adversarial inputs is out of scope.

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