Artificial Intelligence (AI) is often viewed as the means by which the intelligence community will cope with increasing amounts of data. There are challenges in adoption, however, as outputs of such systems may be difficult to trust, for a variety of factors. We conducted a naturalistic study using the Critical Incident Technique (CIT) to identify which factors were present in incidents where trust in an AI technology used in intelligence work (i.e., the collection, processing, analysis, and dissemination of intelligence) was gained or lost. We found that explainability and performance of the AI were the most prominent factors in responses; however, several other factors affected the development of trust. Further, most incidents involved two or more trust factors, demonstrating that trust is a multifaceted phenomenon. We also conducted a broader thematic analysis to identify other trends in the data. We found that trust in AI is often affected by the interaction of other people with the AI (i.e., people who develop it or use its outputs), and that involving end users in the development of the AI also affects trust. We provide an overview of key findings, practical implications for design, and possible future areas for research.