3D perception plays a crucial role in real-world applications such as autonomous driving, robotics, and AR/VR. In practical scenarios, 3D perception models must continuously adapt to new data and emerging object categories, but retraining from scratch incurs prohibitive costs. Therefore, adopting class-incremental learning (CIL) becomes particularly essential. However, real-world 3D point cloud data often include corrupted samples, which poses significant challenges for existing CIL methods and leads to more severe forgetting on corrupted data. To address these challenges, we consider the scenario in which a CIL model can be updated using point clouds with unknown corruption to better simulate real-world conditions. Inspired by Farthest Point Sampling, we propose a novel exemplar selection strategy that effectively preserves intra-class diversity when selecting replay exemplars, mitigating forgetting induced by data corruption. Furthermore, we introduce a point cloud downsampling-based replay method to utilize the limited replay buffer memory more efficiently, thereby further enhancing the model's continual learning ability. Extensive experiments demonstrate that our method improves the performance of replay-based CIL baselines by 2% to 11%, proving its effectiveness and promising potential for real-world 3D applications.