First try to right click the icon and see if you get a connect now option. If so, select it to reconnect. Listed below are some other suggestions from the FAQ on Southwest's DING site.
26. The icon in my system tray shows a connection error, how do I connect?
If you have a connection to the Internet (through dial-up, cable, or DSL) the DING! application should be working properly. If you are showing a connection error, verify that your computer is in fact connected to the Internet. If you verify that you are connected to the Internet, you may have a firewall issue.
27. How can I tell if the connection error is due to a firewall issue?
Open a browser window (ie: Netscape?, Internet Explorer?, etc.) and type in the address ding.southwest.com. If your browser returns DING! help pages then your firewall protection is not causing your connection issue.
28. My firewall is preventing the application from connecting to the Internet, how can I resolve this?
If you are using a personal firewall application (i.e.: Zone Alarm?, Norton Internet Security?, etc.) check your configuration to make sure that access is enabled for the following URLs: southwest.com and ding.southwest.com and that you have allowed access to the DING! program.
If you are using DING! from a work location and you have a connection error, the cause could be your corporate firewall. You will need to contact your Information Technology help desk for assistance. You may ask them to grant you access to the URLs listed above.