Multi-view 3D reconstruction applications are revolutionizing critical use cases that require rapid situational-awareness, such as emergency response, tactical scenarios, and public safety. In many cases, their near-real-time latency requirements and ad-hoc needs for compute resources necessitate adoption of `Just-in-time' edge environments where the system is set up on the fly to support the applications during the mission lifetime. However, reliability issues can arise from the inherent dynamism and operational adversities of such edge environments, resulting in spatiotemporally correlated disruptions that impact the camera operations, which can lead to sustained degradation of reconstruction quality. In this paper, we propose a novel portfolio theory inspired edge resource management strategy for reliable multi-view 3D reconstruction against possible system disruptions. Our proposed methodology can guarantee reconstruction quality satisfaction even when the cameras are prone to spatiotemporally correlated disruptions. The portfolio theoretic optimization problem is solved using a genetic algorithm that converges quickly for realistic system settings. Using publicly available and customized 3D datasets, we demonstrate the proposed camera selection strategy's benefits in guaranteeing reliable 3D reconstruction against traditional baseline strategies, under spatiotemporal disruptions.