With the proliferation of Low Earth Orbit (LEO) spacecraft constellations, comes the rise of space-based wireless cognitive communications systems (CCS) and the need to safeguard and protect data against potential hostiles to maintain widespread communications for enabling science, military and commercial services. For example, known adversaries are using advanced persistent threats (APT) or highly progressive intrusion mechanisms to target high priority wireless space communication systems. Specialized threats continue to evolve with the advent of machine learning and artificial intelligence, where computer systems inherently can identify system vulnerabilities expeditiously over naive human threat actors due to increased processing resources and unbiased pattern recognition. This paper presents a disruptive abuse case for an APT-attack on such a CCS and describes a trade-off analysis that was performed to evaluate a variety of machine learning techniques that could aid in the rapid detection and mitigation of an APT-attack. The trade results indicate that with the employment of neural networks, the CCS s resiliency would increase its operational functionality, and therefore, on-demand communication services reliability would increase. Further, modelling, simulation, and analysis (MS\&A) was achieved using the Knowledge Discovery and Data Mining (KDD) Cup 1999 data set as a means to validate a subset of the trade study results against Training Time and Number of Parameters selection criteria. Training and cross-validation learning curves were computed to model the learning performance over time to yield a reasonable conclusion about the application of neural networks.