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 demonstrate that AEGIS enhances timely-service continuity, contains persistent deadline violations, and improves post-stress recovery through adaptive cross-time risk regulation. Meanwhile, it effectively controls predicted-risk exposure while preserving competitive service performance, achieving a favorable balance between service resilience and risk control.

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