While retrieval is a core function of vision-language models, continually updating these models for retrieval tasks remains critically underexplored. Existing work often approaches continual retrieval through the lens of class-incremental learning (CIL), evaluating both standard CIL methods and retrieval-oriented adaptations in settings that may not fully capture the retrieval-specific dynamics. To address this, we introduce a new, principled evaluation framework for continual multimodal retrieval (CMR) spanning diverse visual domains, and systematically evaluate common approaches within this setting. Our empirical analysis shows that standard CIL methods fail to yield meaningful gains in our more challenging scenario. Therefore, we propose Dynamic Adapter Routing (DAR), a novel approach based on adapters selected through prototype-based routing and combined via model merging.DAR achieves superior performance over the previous baselines and demonstrates strong generalization under out-of-distribution evaluation. Our results highlights the unique challenges of CMR and encourages further research in this direction.