LiDAR-based localization and mapping is one of the core components in many modern robotic systems due to the direct integration of range and geometry, allowing for precise motion estimation and generation of high quality maps in real-time. Yet, as a consequence of insufficient environmental constraints present in the scene, this dependence on geometry can result in localization failure, happening in self-symmetric surroundings such as tunnels. This work addresses precisely this issue by proposing a neural network-based estimation approach for detecting (non-)localizability during robot operation. Special attention is given to the localizability of scan-to-scan registration, as it is a crucial component in many LiDAR odometry estimation pipelines. In contrast to previous, mostly traditional detection approaches, the proposed method enables early detection of failure by estimating the localizability on raw sensor measurements without evaluating the underlying registration optimization. Moreover, previous approaches remain limited in their ability to generalize across environments and sensor types, as heuristic-tuning of degeneracy detection thresholds is required. The proposed approach avoids this problem by learning from a collection of different environments, allowing the network to function over various scenarios. Furthermore, the network is trained exclusively on simulated data, avoiding arduous data collection in challenging and degenerate, often hard-to-access, environments. The presented method is tested during field experiments conducted across challenging environments and on two different sensor types without any modifications. The observed detection performance is on par with state-of-the-art methods after environment-specific threshold tuning.