Answer
Labels for a feature service created in ArcGIS Online display in the ArcGIS Online map viewer. However, when the web map is saved, these labels are not displayed in client applications such as ArcMap, Flex Viewer, or Silverlight. Labels are properties of the ArcGIS Online map viewer. When labels are created, a map uses JavaScript Object Notation (JSON) to store the information. If the web map is saved, the JSON is saved and can only be accessed via the web map. If the layer is saved with the respective changes made to the labels, then ArcGIS Online as an application records and recalls the labels and applies them automatically.
However, when using the service outside ArcGIS Online as a client application, the label reference information is lost because saving the layer information does not alter the service itself. This is because when layers are saved from the web, references to the layers and the properties that users configured are saved, but not the actual data.
Users may use ArcGIS for Server to create permanent labels in a service.