In recent years, most 3D point cloud analysis models have focused on developing either new network architectures or more efficient modules for aggregating point features from a local neighborhood. Regardless of the network architecture or the methodology used for improved feature learning, these models share one thing, which is the use of max-pooling in the end to obtain permutation invariant features. We first show that this traditional approach causes only a fraction of 3D points contribute to the permutation-invariant features, and discards the rest of the points. In order to address this issue and improve the performance of any baseline 3D point classification or segmentation model, we propose a new module, referred to as the Recycling Max-Pooling (RMP) module, to recycle and utilize the features of some of the discarded points. We incorporate a refinement loss that uses the recycled features to refine the prediction loss obtained from the features kept by traditional max-pooling. To the best of our knowledge, this is the first work that explores recycling of still useful points that are traditionally discarded by max-pooling. We demonstrate the effectiveness of the proposed RMP module by incorporating it into several milestone baselines and state-of-the-art networks for point cloud classification and indoor semantic segmentation tasks. We show that RPM, without any bells and whistles, consistently improves the performance of all the tested networks by using the same base network implementation and hyper-parameters. The code is provided in the supplementary material.