The exclusion of high-motion participants can reduce the impact of motion in functional Magnetic Resonance Imaging (fMRI) data. However, the exclusion of high-motion participants may change the distribution of clinically relevant variables in the study sample, and the resulting sample may not be representative of the population. Our goals are two-fold: 1) to document the biases introduced by common motion exclusion practices in functional connectivity research and 2) to introduce a framework to address these biases by treating excluded scans as a missing data problem. We use a study of autism spectrum disorder to illustrate the problem and the potential solution. We aggregated data from 545 children (8-13 years old) who participated in resting-state fMRI studies at Kennedy Krieger Institute (173 autistic and 372 typically developing) between 2007 and 2020. We found that autistic children were more likely to be excluded than typically developing children, with 29.1% and 16.1% of autistic and typically developing children excluded, respectively, using a lenient criterion and 80.8% and 59.8% with a stricter criterion. The resulting sample of autistic children with usable data tended to be older, have milder social deficits, better motor control, and higher intellectual ability than the original sample. These measures were also related to functional connectivity strength among children with usable data. This suggests that the generalizability of previous studies reporting naïve analyses (i.e., based only on participants with usable data) may be limited by the selection of older children with less severe clinical profiles because these children are better able to remain still during an rs-fMRI scan. We adapt doubly robust targeted minimum loss based estimation with an ensemble of machine learning algorithms to address these data losses and the resulting biases. The proposed approach selects more edges that differ in functional connectivity between autistic and typically developing children than the naïve approach, supporting this as a promising solution to improve the study of heterogeneous populations in which motion is common.