National Convective Weather Forecast (NCWF) Java Tool applet not working with Java 7

Reported by a user on java.com:

Environment: Java version: 7
Last working version: 6u33

OS:
  Windows XP/Vista and Mac
  I reproduced this on Mac 10.9 and the site lists XP and Vista. The site also says that one can use Win7 as an alternative, though it seems odd the failure would be see on XP/Vista but not 7.

Text from site: http://bcaws.aviationweather.gov/adds/convection/java/
NOTE: The recent release of Java (ver 1.7) breaks the ADDS Java applets on Windows XP and Vista.
We recommend that users either switch to the Flight Path Tool and select the Convection layer,
revert XP/Vista back to Java 1.6 or use Windows 7. Oracle Java 6 archives

Browser:
      Does not seem related to the browser.

Name of the applet: National Convective Weather Forecast (NCWF)
                http://bcaws.aviationweather.gov/adds/convection/java/
                                                                        

Bug description:
Applet starts then shows message on screen:
"Could not get convective interest data from server. Data Feed Down."

Steps to reproduce:
Go to http://bcaws.aviationweather.gov/adds/convection/java/
Applet will load in page.

Console output that looks related:
network: Connecting http://bcaws.aviationweather.gov/DsServerTunnel with cookie "PHPSESSID=0sov9l9d66jitsq45j9fg6j8k3"
IO exception getting InputStream while sending msg: java.io.FileNotFoundException: http://bcaws.aviationweather.gov/DsServerTunnel
Error: Could not get gen time from server.
Error: Couldn't get latest grid time from server.