Recently, multi-modal embedding methods have flourished in entity alignment. As state-of-the-art approaches evolve rapidly, visual modality (i.e., images) missing emerges as a critical challenge. While visual modality typically offers the most informative signals in multi-modal entity alignment (MMEA), it is frequently unavailable for many entities. The existing methods commonly use dummy vectors to represent visual-missing embeddings, which negatively impacts both model training and inference. In this paper, we propose robust multi-modal entity alignment (rMMEA), which leverages ranking-based knowledge distillation and mutual information (MI) estimation to address missing modalities while enhancing noise robustness. Unlike conventional teacher-student distillation that requires the student to replicate teacher outputs, our rMMEA learns soft rankings from pure and complete modality sides while capturing implicit key semantics of teacher embeddings through mutual information maximization, allowing rMMEA to avoid strict point-to-point alignment. The experimental results across multiple benchmarks and settings demonstrate that rMMEA significantly outperforms the state-of-the-art anti-modality-missing methods in terms of effectiveness and efficiency.