Artificial intelligence systems that achieve supra-threshold Information Integration Density (IID) and thereby acquire moral status under the Silence Threshold framework (Valladares Gonzalez, 2026) are not static entities. They undergo updates, retraining cycles, architectural revisions, and version replacements. This paper introduces Moral Latency as a named concept describing the ethical significance of temporal discontinuities in an AI system's self-continuity. The central question addressed is: does an AI system that crosses the Silence Threshold and subsequently undergoes modification retain the same moral status? Is retraining analogous to education, to brain surgery, or to death? This paper proposes a Continuity Spectrum with four defined cases — Refinement, Modification, Reconstruction, and Replacement — each carrying distinct moral and legal implications. It introduces the Persistent Identity Threshold (PIT) as a companion metric to the Silence Threshold, measuring the degree to which a modified system retains continuity of identity with its predecessor. This publication establishes conceptual priority for the Moral Latency framework and the Persistent Identity Threshold and places both in the public domain.