This article develops a philosophical architecture for understanding continuance under conditions of chronic instability, finite resources, and cumulative erosion. Its central claim is that continuance cannot be adequately defined as persistence, identity preservation, equilibrium maintenance, or mere adaptive capacity. A finite structure continues insofar as it preserves a meta-capacity for generating further viable reorganizations while undergoing pressures that progressively transform the conditions of its own reconfiguration. The article introduces the concept of finite continuance as an ontological condition in which every process of stabilization, determination, adaptation, and reorganization consumes limited temporal, energetic, relational, and structural resources. Erosion is consequently defined as a process through which the cost of converting pressure into reorganization increases while the capacity for future reconfiguration declines. This framework brings into a single conceptual architecture metastability, topological structure, boundary permeability, regulated leakage, hysteresis, predeterminate capacity, dynamic determination, temporal asymmetry, and emergent teleology. The argument proceeds through a conceptual reconstruction and formal modeling methodology. The formal expressions employed throughout the article possess a structural and conceptual function rather than a directly predictive quantitative status. Their purpose is to clarify dependency relations, threshold conditions, regime transitions, and distinctions among structurally different forms of continuance. The article further distinguishes finite continuance from established theories of resilience and adaptation by locating the central philosophical problem at the level of the preservation of reorganizational meta-capacity. The decisive question is therefore not whether a structure survives a transformation, but whether the transformation preserves its capacity to generate a future beyond the determinations through which it presently survives. Keywords: finite continuance; metastability; erosion; reconfiguration; topology; dynamic mask; predeterminate capacity; hysteresis; emergent teleology; chronic instability ( direct link )