I think I'm getting the same problem as well. When I try to connect directly to a feature layer within a map service, using the fully qualified URL, I get the "cannot connect to..." error. If navigate to the feature layer by browsing from the ".../rest/services" service directly, it throws a javascript (JSON) error.
When I select the entire Map Service, I am able to connect, however I only get the image data. All of the tools related to data query are greyed out.