Entanglement preservation in noisy quantum memories represents a long-standing conceptual challenge in quantum information science. While experiments have shown that electromagnetically induced transparency (EIT) memories can store entangled photons, a rigorous theoretical demonstration of whether such memories fundamentally preserve nonlocality has remained elusive. Here we develop a unified open-system model that combines the dark-state polariton formalism with reduced density operator theory to describe the retrieved photon state under realistic ground state decoherence. The analysis reveals that decoherence inevitably transforms an initially pure Bell state into a mixed state and predicts a critical storage efficiency threshold of 89.7%. Above this threshold, the retrieved photon violates the Clauser-Horne inequality, confirming the preservation of nonlocal quantum correlations, whereas below it, nonlocality is lost. This work provides the first systematic theoretical proof that EIT quantum memories can in principle preserve entanglement and nonlocality, thereby resolving a fundamental question in the physics of quantum information storage.