Question: "What repeated phrase suggests that it is critical?"

Context: "The SCN projects to a set of areas in the hypothalamus, brainstem, and midbrain that are involved in implementing sleep-wake cycles. An important component of the system is the reticular formation, a group of neuron-clusters scattered diffusely through the core of the lower brain. Reticular neurons send signals to the thalamus, which in turn sends activity-level-controlling signals to every part of the cortex. Damage to the reticular formation can produce a permanent state of coma."

Answer:
reticular formation
The phrase "reticular formation" is used twice in the passage. The reticular neurons are described as having a specific function, and damage to them can result in coma. This suggests that it's an important component of controlling activity levels throughout our brain and body..