This paper introduces the Law of Non-Bypassable Governance, a structural principle governing the stability of long-lived systems that internalize decision authority while operating under cumulative pressure. It identifies a critical boundary condition—the Internalized Decision Authority Threshold (IDAT)—beyond which system requirements change qualitatively. The central claim is that once a system crosses IDAT, stability cannot be preserved through policy, oversight, alignment techniques, or post-hoc correction alone. Instead, governing constraints must be enforced as structurally non-bypassable invariants that restrict the system’s reachable state space by construction. When governance remains bypassable, instability becomes inevitable under sufficient pressure and time. The paper develops this claim through: a formal definition of IDAT, a minimal mathematical characterization of decision authority, continuity, pressure, and governance, a phase-space model explaining delayed and catastrophic failure modes, cross-domain validation using biological immune regulation and fire-adapted ecological systems, and a concrete operating-system case study demonstrating the feasibility of post-IDAT governance via kernel-level invariant enforcement. The law is independent of intelligence, consciousness, ethical reasoning, or implementation substrate, and applies to artificial, biological, ecological, and institutional systems alike. The work reframes safety and governance as architectural necessities rather than behavioral or ethical problems, and provides a foundation for the design of stable autonomous systems operating beyond IDAT.