Hi Bob,
One of the cause could be the coordinates sent would be in different spatial reference than what is expected by server.
Could you capture HTTP REST request and response(using firebug/fiddler) to see whats going on behind the scenes?
Flex api communicates with the server using REST API and sniffer tool such as Firebug /Fiddler captures that communicationa. Using that requuest we could take the Flex API out of the picture and send REST request directly using Browser and see if its working or not.
If you could captuire REST request/ response that would be helpful to find the cause...
Mehul