Contemporary deep neural networks offer stateof-the-art results when applied to visual reasoning, e.g., in the context of 3D point cloud data. Point clouds are important datatype for precise modeling of three-dimensional environments, but effective processing of this type of data proves to be challenging. In the world of large, heavily-parameterized network architectures and continuously-streamed data, there is an increasing need for machine learning models that can be trained on additional data. Unfortunately, currently available models cannot fully leverage training on additional data without losing their past knowledge. Combating this phenomenon, called catastrophic forgetting, is one of the main objectives of continual learning. Continual learning for deep neural networks has been an active field of research, primarily in 2D computer vision, natural language processing, reinforcement learning, and robotics. However, in 3D computer vision, there are hardly any continual learning solutions specifically designed to take advantage of point cloud structure. This work proposes a novel neural network architecture capable of continual learning on 3D point cloud data. We utilize point cloud structure properties for preserving a heavily compressed set of past data. By using rehearsal and reconstruction as regularization methods of the learning process, our approach achieves a significant decrease of catastrophic forgetting compared to the existing solutions on several most popular point cloud datasets considering two continual learning settings: when a task is known beforehand, and in the challenging scenario of when task information is unknown to the model.