This message can sometimes show even when you have a good internet connection, if you navigate to the Messages section and quickly click the New Message button, before the call comes back from the server.
I can understand that this message, if displayed when you have a good internet connection, can be misleading. If you close the message window and open it again, this message will go away (or wait a moment). We're working on better ways to determine a good connection to our servers.
Important note: At this time, secure messaging does not function using IE9. We recommend that patients use Chrome or Firefox as their web browser.