Hi Jeff,
For starters, is it safe to assume that when you initially published your service, you allowed for Feature Access?
https://doc.arcgis.com/en/arcgis-online/share-maps/publish-features.htm#ESRI_SECTION1_94021BE7D87547...
and see number 7. (I believe you will want to check the box for "Query" as well).
Also, in the properties of the feature service in ArcGIS Online, have you configured your feature search to allow searching the feature service based on an attribute?
Configure feature search—ArcGIS Online Help | ArcGIS
I would think with all of the taken care of, then you should be able to see more results in your configured search in your basic viewer map. At least, I hope so.