When backing up data from ArcGIS Online for Organizations, exporting feature layers with a large number of attachments to a file geodatabase results in an error or in missing feature layer attachments.
This is a known issue.
Create a replica from the REST endpoint of the hosted feature service, and download the file geodatabase in a ZIP file format.
Instructions are available in the following Esri Knowledge Base article:
HowTo: Retrieve attachments from a hosted feature service