Including Feature Service in geoprocessing task

I have successfully published a feature service task, providing 3 feature classes (2 point layers and 1 polyline layers). And I access the service from an JavaScript Web application. I would like to use the polyline feature class in an additional geoprocessing task. By creating the geoprocessing model in the modelbuilder, i select the desired polyline-feature class, from a database connection at the "Database Connections" folder. After publishing the geoprocessing task, i get the following error message: "The value does not exist. ERROR 000732: Input Features: Dataset Database Connections\Connection to servername.sde\feature_class_name does not exist or is not supported"

I guess that's because publishing the geoprocessing task doesn't include the connection to the database server?? how can a feature service be included to the geoprocessing task?

The work around of loading the feature class, by the web application, and sending it to the geoprocessing task, generates of cours hugh transfer data.

best regards from germany,
Tom