Across all ages, individuals with Down syndrome (DS) experience high rates of sleep problems as well as cognitive impairments. This study sought to investigate whether circadian rhythm disruption was also experienced by people with DS and whether this kind of sleep disorder may be correlated with cognitive performance. A cross-sectional study of 101 participants (58 with DS, 43 with typical development) included individuals in middle childhood (6–10 years old), adolescence (11–18 years old), and young adulthood (19–26 years old). Sleep and markers of circadian timing and robustness were calculated using actigraphy. Cognitive and behavioral data were gathered via a novel touchscreen battery (A-MAP^TM, Arizona Memory Assessment for Preschoolers and Special Populations) and parent questionnaire. Results indicated that children and adolescents with DS slept the same amount as peers with typical development, but significant group differences were seen in phase timing. The circadian robustness markers, interdaily stability and intradaily variability of sleep-wake rhythms, were healthiest for children regardless of diagnostic group and worst for adults with DS. Amplitude of the 24-h activity profile was elevated for all individuals with DS. In analyses of the correlations between sleep quality, rhythms, and cognition in people with DS, interdaily stability was positively correlated with reaction time and negatively correlated with verbal and scene recall, a finding that indicates increased stability may paradoxically correlate with poorer cognitive outcomes. Further, we found no relations with sleep efficiency previously found in preschool and adult samples. Therefore, the current findings suggest that a thorough examination of sleep disorders in DS must take into account age as well as circadian robustness to better understand sleep-cognitive correlations in this group.