I've ran across this issue and there is a bug:
BUG-000131082
Synopsis: Unable to download data of a referenced feature service from ArcGIS Enterprise Sites.
I believe the bug is currently being looked at. Additionally, I've recently discovered if you share a referenced feature layer to ArcGIS Portal's Enterprise Sites, be certain the "Export Data" option is toggled on in the Share Configuration options. When you navigate to the Sites download source, you now have the option to download, but the download itself is not working for me. The Download meter goes to 150% (instead of 100%) and when you download the data, you may receive a Compressed Folder error.
Hope this helps.