Neural distance fields offer a compact and continuous representation of 3D geometry, making them attractive for incremental LiDAR mapping. However, their online optimization is vulnerable to catastrophic forgetting, where new observations can degrade previously reconstructed geometry. Replay-based training is commonly used to address this issue, but existing methods typically rely on passive replay buffers and uniform sampling, which can waste memory on redundant observations and under-train poorly constrained regions. We propose LAPS, a replay management framework for incremental neural mapping that improves both replay retention and replay allocation during online updates. LAPS combines reliability-based active pooling to retain reliable historical samples under limited memory with uncertainty-guided active sampling to focus optimization on under-constrained regions. Experiments on synthetic and real-world benchmarks show that LAPS consistently improves reconstruction completeness while maintaining competitive geometric accuracy. On Oxford Spires, it improves recall by 4.66 pp and F1-score by 3.79 pp over PIN-SLAM on the Blenheim Palace 05 sequence. We release our open source implementation at: https://github.com/dongjae0107/LAPS.