Hypergraph contrastive learning has emerged as a powerful unsupervised paradigm for hypergraph representation learning. Traditional hypergraph contrastive learning methods typically leverage neighbor aggregation strategy to obtain entity (node and hyperedge) representations within each connected component, and then utilize contrastive losses (e.g., node- or hyperedge-level) to update the encoders. However, since entities are usually focused equally on their respective losses, large connected components with numerous entities tend to provide a dominant contribution to the whole learning process, which inevitably hinders the effective learning of entity representations within small connected components. To address this issue, we propose a novel Connected-Component-Aware Hypergraph Contrastive Learning method (CCAHCL). Different from previous methods that only construct node or hyperedge representations, our method additionally constructs the connected component representations, and accordingly designs a hierarchical contrastive loss to balance the model's focus on different scales of connected components. Specifically, we first use the traditional neighbor aggregation strategy to aggregate and update entity (node and hyperedge) representations. Then, these entity representations are further aggregated to generate the connected component representations, where entity features are incorporated into connected components and their structural information is propagated back to enrich their corresponding entities. Afterwards, we employ node-level and hyperedge-level losses to learn the enriched entity representations, and further propose a novel connected-component-level contrastive loss to balance the model's focus on all different connected components, naturally avoiding the learning bias on large connected components. Extensive experiments on various datasets demonstrate that our proposed model achieves superior performance against other state-of-the-art methods.