As AI systems increasingly generate recommendations, explanations, summaries, and classifications within regulated and fiduciary workflows, organizations face a growing evidentiary gap: they are often unable to reconstruct what an AI system presented at the moment its output could have influenced a decision. Existing AI governance mechanisms emphasize model oversight, explainability, and monitoring, yet do not reliably preserve AI-generated representations as inspectable evidence. This paper defines AI Reliance Logging as a distinct evidentiary control class concerned with the systematic capture and preservation of externally observable AI outputs that may later become the object of reliance. It clarifies the procedural failure mode this control addresses, distinguishes it from adjacent governance practices, and situates it within established audit, legal, and disclosure oversight doctrine. The paper is implementation-agnostic and does not prescribe a specific technical solution, focusing instead on the evidentiary obligation that emerges as AI systems increasingly mediate consequential decisions.