Point processes have been dominant in modeling the evolution of seismicity for decades, with the Epidemic Type Aftershock Sequence (ETAS) model being most popular. Recent advances in machine learning have constructed highly flexible point process models using neural networks to improve upon existing parametric models. We investigate whether these flexible point process models can be applied to short-term seismicity forecasting by extending an existing temporal neural model to the magnitude domain and we show how this model can forecast earthquakes above a target magnitude threshold. We first demonstrate that the neural model can fit synthetic ETAS data, however, requiring less computational time because it is not dependent on the full history of the sequence. By artificially emulating short-term aftershock incompleteness in the synthetic dataset, we find that the neural model outperforms ETAS. Using a new enhanced catalog from the 2016-2017 Central Apennines earthquake sequence, we investigate the predictive skill of ETAS and the neural model with respect to the lowest input magnitude. Constructing multiple forecasting experiments using the Visso, Norcia and Campotosto earthquakes to partition training and testing data, we target M3+ events. We find both models perform similarly at previously explored thresholds (e.g., above M3), but lowering the threshold to M1.2 reduces the performance of ETAS unlike the neural model. We argue that some of these gains are due to the neural model's ability to handle incomplete data. The robustness to missing data and speed to train the neural model present it as an encouraging competitor in earthquake forecasting.