Removing a sublayer from the map image service in Map Viewer, saving the layer, and then overwriting the service causes the removed service layer to not display in the content list when creating a new web with the same service.
This defect was logged against a no longer supported version of the software. The issue is not reproducible in Map Viewer in the newer versions of ArcGIS Enterprise 10.9 and higher. If the issue persists, contact Esri Support Services as a new reproduction case is needed to continue the investigation.