In 2015, an estimated 1.3 million intrapartum stillbirths occurred, meaning that the fetus died during labour. The majority of these stillbirths occurred in low and middle income countries. With the introduction of affordable continuous fetal heart rate (FHR) monitors for use in these settings, the fetal well-being can be better monitored and health care personnel can potentially intervene at an earlier time if abnormalities in the FHR signal are detected. Additional information about the fetal health can be extracted from the fetal heart rate signals through signal processing and analysis. A challenge is, however, the large number of missing samples in the recorded FHR as fetal and maternal movement in addition to sensor displacement can cause data dropouts. Previously proposed methods perform well on estimation of short dropouts, but struggle with data from wearable devices with longer dropouts. Sparse representation and dictionary learning have been shown to be useful in the related problem of image inpainting. The recently proposed dictionary learning algorithm, SI-FSDL, learns shift-invariant dictionaries with long atoms, which could be beneficial for such time series signals with large dropout gaps. In this paper it is shown that using sparse representation with dictionaries learned by SI-FSDL on the FHR signals with missing samples provides a reconstruction with improved properties compared to previously used techniques.