I had the same issue when publishing a point feature class rendered at 12 point within the ArcGIS Pro session (45 pixel size in web map) and published to Portal. The 'pop-up click sensitivity radius' or 'hit box' performed fine in the mapping session but when published the user had to click the center of the point in order for the pop-up to open otherwise was met with a no data message.
The fix (solved by one of my brilliant colleagues) was to work with the 'feature layer service' rather than the map service layer ('https://mapserviceURL' vs 'https://mapserviceURL/0'). The reason for this appears to be that the map service is rendered on the server side, while the feature service is rendered on the client-side. Map image services serve up images of the data, however feature layer services serve the underlying data itself and allows for editing which entails client-side rendering.
HTH,
Yuri