Continuous edge inference for unmanned aerial vehicles (UAVs) faces uncertain wireless connectivity, competition for shared computing resources, and the overhead of model loading and session-state migration. These interdependent factors complicate request admission and the continuity of successive inference services. This paper investigates joint request admission, edge-server assignment, and model selection under an admission-priority objective that strictly favors any feasible increase in admitted requests over bounded losses in delay, interruption risk, model quality, migration, and deployment. To address this problem, we propose Service-Window-Guided Admission and Model Placement (SWAP), which integrates predictive service-window information with shared model deployment and coordinated scheduling. Quantile regression and probability calibration estimate the remaining service window and interruption risk, while a bounded residence factor characterizes the potential reuse of shared model instances. We then formulate a constrained exact potential game based on marginal-contribution utilities and develop a solution procedure combining unilateral improvement, coordinated admission, and finite binary logit refinement. Theoretical analysis establishes NP-hardness, the existence of a constrained pure Nash equilibrium, and finite descent, together with feasibility and approximate unilateral equilibrium guarantees for the returned assignment. Simulation results demonstrate improved service continuity and reduced request rejection under increasing resource contention, while characterizing the accompanying tradeoffs in model-deployment traffic, inference quality, and execution delay.

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