Multimodal models integrating natural language and visual information have substantially improved emotion recognition performance. However, their effectiveness significantly declines in real-world situations where certain modalities are missing or unavailable. This degradation primarily stems from inconsistent representation learning between complete multimodal data and incomplete modality scenarios. Existing approaches typically address missing modalities through relatively simplistic generation methods, yet these approaches fail to adequately preserve cross-modal consistency, leading to suboptimal performance. To overcome this limitation, we propose a novel multimodal framework named PROMISE, a prompting-Attentive Hierarchical Contrastive Learning approach designed explicitly for robust cross-modal representation under conditions of missing modalities. Specifically, Promise innovatively incorporates multimodal prompt learning into a hierarchical contrastive learning framework, equipped with a specially designed prompting-attention mechanism. This mechanism dynamically generates robust and consistent representations for scenarios where particular modalities are absent, thereby effectively bridging the representational gap between complete and incomplete data. Extensive experiments conducted on benchmark datasets, along with comprehensive ablation studies, clearly demonstrate the superior performance of PROMISE compared to current state-of-the-art multimodal methods.