Incomplete multi-modal medical image segmentation faces critical challenges from modality imbalance, including imbalanced modality missing rates and heterogeneous modality contributions. Due to their reliance on idealized assumptions of complete modality availability, existing methods fail to dynamically balance contributions and neglect the structural relationships between modalities, resulting in suboptimal performance in real-world clinical scenarios. To address these limitations, we propose a novel model, named Dynamic Modality-Aware Fusion Network (DMAF-Net). The DMAF-Net adopts three key ideas. First, it introduces a Dynamic Modality-Aware Fusion (DMAF) module to suppress missing-modality interference by combining transformer attention with adaptive masking and weight modality contributions dynamically through attention maps. Second, it designs a synergistic Relation Distillation and Prototype Distillation framework to enforce global-local feature alignment via covariance consistency and masked graph attention, while ensuring semantic consistency through cross-modal class-specific prototype alignment. Third, it presents a Dynamic Training Monitoring (DTM) strategy to stabilize optimization under imbalanced missing rates by tracking distillation gaps in real-time, and to balance convergence speeds across modalities by adaptively reweighting losses and scaling gradients. Extensive experiments on BraTS2020 and MyoPS2020 demonstrate that DMAF-Net outperforms existing methods for incomplete multi-modal medical image segmentation. Extensive experiments on BraTS2020 and MyoPS2020 demonstrate that DMAF-Net outperforms existing methods for incomplete multi-modal medical image segmentation. Our code is available at https://github.com/violet-42/DMAF-Net.