Edge AI is often framed as model compression and deployment under tight constraints. We argue a stronger operational thesis: Edge AI in realistic deployments is necessarily adaptive. In long-horizon operation, a fixed (non-adaptive) configuration faces a fundamental failure mode: as data and operating conditions evolve and change in time, it must either (i) violate time-varying budgets (latency/energy/thermal/connectivity/privacy) or (ii) lose predictive reliability (accuracy and, critically, calibration), with risk concentrating in transient regimes and rare time intervals rather than in average performance. If a deployed system cannot reconfigure its computation - and, when required, its model state - under evolving conditions and constraints, it reduces to static embedded inference and cannot provide sustained utility. This position paper introduces a minimal Agent-System-Environment (ASE) lens that makes adaptivity precise at the edge by specifying (i) what changes, (ii) what is observed, (iii) what can be reconfigured, and (iv) which constraints must remain satisfied over time. Building on this framing, we formulate ten research challenges for the next decade, spanning theoretical guarantees for evolving systems, dynamic architectures and hybrid transitions between data-driven and model-based components, fault/anomaly-driven targeted updates, System-1/System-2 decompositions (anytime intelligence), modularity, validation under scarce labels, and evaluation protocols that quantify lifecycle efficiency and recovery/stability under drift and interventions.