This paper addresses catastrophic forgetting in mobile edge UAV networks within dynamic spatiotemporal environments. Conventional deep reinforcement learning often fails during task transitions, necessitating costly retraining to adapt to new user distributions. We propose the spatiotemporal continual learning (STCL) framework, realized through the group-decoupled multi-agent proximal policy optimization (G-MAPPO) algorithm. The core innovation lies in the integration of a group-decoupled policy optimization (GDPO) mechanism with a gradient orthogonalization layer to balance heterogeneous objectives including energy efficiency, user fairness, and coverage. This combination employs dynamic z-score normalization and gradient projection to mitigate conflicts without offline resets. Furthermore, 3D UAV mobility serves as a spatial compensation layer to manage extreme density shifts. Simulations demonstrate that the STCL framework ensures resilience, with service reliability recovering to over 0.9 for moderate loads of up to 100 users. Even under extreme saturation with 140 users, G-MAPPO maintains a significant performance lead over the multi-agent deep deterministic policy gradient (MADDPG) baseline by preventing policy stagnation. The algorithm delivers an effective capacity gain of 20 percent under high traffic loads, validating its potential for scalable aerial edge swarms.

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