Automaticity, the ability to perform a task rapidly with minimal effort, plays a key role in reading fluency and is indexed by rapid automatized naming (RAN) and processing speed. Yet little is known about automaticity's neurophysiologic underpinnings. The more efficiently sound is encoded, the more automatic sound processing can be. In turn, this automaticity could free up cognitive resources such as attention and working memory to help build an integrative reading network. Therefore, we hypothesized that automaticity and reading fluency correlate with stable neural representation of sounds, given a larger body of literature suggesting the close relationship between neural stability and the integrative function in the central auditory system. To test this hypothesis, we recorded the frequency-following responses (FFR) to speech syllables and administered cognitive and reading measures to school-aged children. We show that the stability of neural responses to speech correlates with RAN and processing speed, but not phonological awareness. Moreover, the link between neural stability and RAN mediates the previously-determined link between neural stability and reading ability. Children with a RAN deficit have especially unstable neural responses. Our neurophysiological approach illuminates a potential neural mechanism specific to RAN, which in turn indicates a relationship between synchronous neural firing in the auditory system and automaticity critical for reading fluency.