Individuals with congenital amusia have a lifelong history of unreliable pitch processing. Accordingly, they downweight pitch cues during speech perception (even large, obvious ones) and instead rely on other dimensions such as duration. We investigated the neural basis for this strategy. During fMRI, individuals with amusia and controls (N=30) matched auditory and visual sentences using pitch and duration cues. A data-driven analysis procedure detected prominent reductions in functional connectivity in the amusia group, between left prefrontal language-related regions (inferior and middle frontal gyrus/DLPFC) and right hemisphere pitch-related regions (auditory and anterior insular cortex). Functional connectivity levels were correlated with prosodic cue weights measured outside the scanner. Furthermore, group differences in functional connectivity between these regions was not present during a control task (passive listening to tones). Our results suggest that individuals compensate for differences in the reliability of perceptual dimensions by regulating functional connectivity between task-relevant frontal and perceptual regions.