Neural implicit surface representations are a promising new development in surfacemodeling. However, the challenges inherent in training neural networks in a continual fashion are still holding them back from being widely used in real-time, incremental scene mapping. We propose a method for learning a neural representation of a signed distance function from trajectories of posed depth images that is both computationally efficient and avoids the problem of catastrophic forgetting. We demonstrate our approach by producing high-quality scene reconstructions in 2D and 3D and incrementally building 2D neural-implicit maps.