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Electronic switches based on the migration of high-density point defects, or memristors, are poised to revolutionize post-digital electronics. Despite significant research, key mechanisms for filament formation and oxygen transport remain unresolved, hindering our ability to predict and design device properties. For example, experiments have achieved 10 orders of magnitude longer retention times than predicted by current models. Here, using electrical measurements, scanning probe microscopy, and first-principles calculations on tantalum oxide memristors, we reveal that the formation and stability of conductive filaments crucially depend on the thermodynamic stability of the amorphous oxygen-rich and oxygen-poor compounds, which undergo composition phase separation. Including the previously neglected effects of this amorphous phase separation reconciles unexplained discrepancies in retention and enables predictive design of key performance indicators such as retention stability. This result emphasizes non-ideal thermodynamic interactions as key design criteria in post-digital devices with defect densities substantially exceeding those of today’s covalent semiconductors.