Maintaining contact in non-prehensile manipulation requires more than nominal friction cone feasibility: a force barely inside the cone and one well inside it are both feasible, but they provide different margins against slip and contact loss. This paper uses signed friction distance to measure friction margin in force space and derives a task-adaptive margin from the force correction needed to balance pivot moment deviations in bimanual tilting. The resulting contact margins are embedded in a sequence of second-order cone programs (SOCPs), each giving a globally optimal contact force solution at a tilt angle. The optimizer balances the object about an environmental pivot while keeping robot and pivot contact forces away from the nominal friction boundary. Optimizer-level results show interpretable force redistribution and adaptation to object property changes. Real-world experiments demonstrate successful execution under object property variations and model mismatch, while fixed margin and no-margin comparisons illustrate the importance of adapting the margin to task demand. These results support signed friction distance margins as a force planning mechanism for maintaining contact in bimanual non-prehensile manipulation. Project page: https://keeping-contact.github.io/

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