The use of massively parallel sequencing of maternal cfDNA for non-invasive prenatal testing (NIPT) of aneuploidy is widely available. Recently, the scope of testing has increased to include selected subchromosomal abnormalities, but the number of samples reported has been small. We developed a calling pipeline based on a segmentation algorithm for the detection of these rearrangements in maternal plasma. The same read depth used in our standard pipeline for aneuploidy NIPT detected 15/18 (83%) samples with pathogenic rearrangements > 6 Mb but only 2/10 samples with rearrangements < 6 Mb, unless they were maternally inherited. There were two false-positive calls in 534 samples with no known subchromosomal abnormalities (specificity 99.6%). Using higher read depths, we detected 29/31 fetal subchromosomal abnormalities, including the three samples with maternally inherited microduplications. We conclude that test sensitivity is a function of the fetal fraction, read depth, and size of the fetal CNV and that at least one of the two false negatives is due to a low fetal fraction. The lack of an independent method for determining fetal fraction, especially for female fetuses, leads to uncertainty in test sensitivity, which currently has implications for this technique’s future as a clinical diagnostic test. Furthermore, to be effective, NIPT must be able to detect chromosomal rearrangements across the whole genome for a very low false-positive rate. Because standard NIPT can only detect the majority of larger (>6 Mb) chromosomal rearrangements and requires knowledge of fetal fraction, we consider that it is not yet ready for routine clinical implementation.