High-powered connected autonomous vehicles (CAVs) with excellent situational awareness are expected to achieve fully autonomous driving. With the increase of complex CAV applications, it is necessary to introduce an effective cooperation mechanism among differentiated edge nodes to provide a complete set of closed-loop control for sophisticated computing tasks. However, when leveraging edge intelligence (EI) for CAVs, neural networks are vulnerable to transient invalidation of edge nodes or transmission links, which may result in serious decision faults. In this article, we first summarize and analyze three situations that trigger transient changes in edge resources, that is, the invalid node, the departure node, and the bottleneck node. To tackle these problems, we propose a novel framework of robust intelligent edge computing orchestrator (RIECO) for CAV networks, which can maintain effectiveness in topology identification and closed-loop control. Importantly, to quickly recover from transient phenomena, the emergency plane proactively migrates defunct models to new nodes. To prove the feasibility of the proposed RIECO framework, we take a series of simulation experiences for different transient scenarios. Finally, some open challenges and future research directions are discussed.