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The benefits of platooning, e.g., fuel efficiency, road throughput enhancement, driver offload, etc., have sparked an interest in a more connected, intelligent, and sustainable transportation ecosystem. However, efficient platooning is realized through wireless communications, characterized by transient connectivity, which is caused by occasional packet losses. Being a safety-critical system of systems, a platoon must be fail-operational even during transient connectivity. Moreover, a platoon should be capable of transitioning into a fail-safe state upon encountering a hazard. To this end, we propose a strategy for classifying the transient communication outages incurred by platooning vehicles into states. Furthermore, a state machine using these states to enable safe automated platooning is proposed that also defines the transitions between the states based on the nature and levels of transient connectivity and hazards. To achieve this, a graceful degradation and upgradation method is proposed, such that the platoon can remain fail-operational by adjusting, e.g., the automated controller and/or the inter-vehicle gaps based on the current communication quality. An emergency braking strategy is also proposed to enable a fast transition into a fail-safe state, should the platoon encounter a hazard. Rigorous simulation studies show that the proposed strategies enable fault-tolerant automated platooning also during transient connectivity.