Continuous edge inference requires sustained wireless and computing support across successive service instances. Under recurring channel degradation, transient edge overload, and multi-user contention, isolated deadline misses may accumulate into persistent service degradation. Existing schedulers mainly optimize instantaneous latency or per-timeslot utility and provide limited control over such cross-time effects. To address this issue, we propose AEGIS (Adaptive Exposure-Governed Inference Scheduling), a risk-budgeted online framework for service-level operational resilience. AEGIS regulates predicted deadline-risk exposure through dynamically replenished per-user risk budgets and establishes an explicit finite-horizon bound on cumulative admitted-risk exposure. One-step state estimation supports anticipatory delay and risk assessment, while the centralized bandwidth-computing allocation is transformed into an exact-potential formulation and solved through asynchronous coordinate updates. Simulation results under varying system scales and stress conditions show that adaptive replenishment improves service continuity and recovery relative to fixed replenishment, while risk budgeting reduces predicted-risk exposure compared with more aggressive scheduling alternatives.

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