Hi Mike,
When you are editing a feature layer hosted in ArcGIS Online, you are editing web enabled geospatial data that is hosted on the cloud. This data is copied and published during the publishing process, resulting in a copy of the data residing in the ArcGIS Online databases. For this reason, after publishing your initial dataset, the source data won't be aware of any changes that happen to the feature layer. If you want to export a file geodatabase of the feature layer, try using any of these tools :
Use layers—ArcGIS Online Help | ArcGIS
Extract Data—ArcGIS Online Help | ArcGIS
-Kelly