Re-installing Skype over your current version installed won't affect your contacts and chat history. But it also won't restore the Skype desktop icon.
To restore it, find the Skype icon/shortcut in the Start menu then right click it. Mouse over Send To and select Desktop (create Shortcut).
I tried your approach and it did not work. Do I have to shut down? Why did the icon go away when I downloaded an update? The shortcut on the toolbar(?) at the bottom says last update 5/9/11/.
I have lost my skype icon from desktop thought of re-installing don't wish to lose my contacts please help
Can you see Skype icon in Windows Start -> All Programs -> Skype?
Reinstall latest Skype
If still the issue persists,
Then go to Skype folder inside program files and go to phone folder and then right click on Skype application and select send to Desktop (Create shortcut)
Please note that, Contacts list are stored on Skype server.