When Continuation Fails Without Stopping

Processes can persist while failing to support their own continuation. In such cases, states remain observable, yet no longer function as conditions for further unfolding. This paper argues against the claim that persistence, regularity, and indefinite extension suffice for continuation. It isolates a condition under which what is ordinarily taken as continuation can fail, and identifies a boundary beyond which that condition becomes unstable and fails. A minimal counterexample shows that a process may remain stable, regular, and indefinitely extended while no longer sustaining further development. The result is a constraint on when continuation is available.