Feature layers don't support labeling. To understand why, you need to understand how these different layer types work.
Map Services - Layers based on map services are drawn by the server and return an image to client applications, like arcgis.com, to display. ArcGIS.com gets the image, with all the labeling. Basically the server has all the power to draw, just like ArcMap does. The complex labeling of ArcMap is essentially part of the image that gets returned.
Feature Services - layers based on feature services are drawn by client applications. A client, like ArcGIS.com sends a request to the server and instead of getting a nicely drawn image back, the server returns lists of coordinates and attributes for each feature, with some drawing instructions. No labeling. It's up to the client to draw the layer as best as it can. Clients like web browsers have very primitive drawing abilities. This is also why complex point, line and polygon symbology is not available to layers based on feature services.
Hope this helps,
Mike