There are a few things to check.
First, in the Windows Service Manager (Control Panel -> Administrative tools -> Services), can you check if the WebClient service is running? If it is not, please start it and set it to "Automatic" so that it starts whenever you reboot your machine. And then restart the drive mapping service.
Second, the Windows XP WebDav driver requires that the mapped drive has to run using port 80. Sometimes, the mapped drive is unable to obtain that port.
There are two common known causes of this:
1. IIS web-server
For IIS, the solution depends on how the user is using IIS. If IIS is being used to serve a website to external clients (ie. over a specific IP), you can configure the web-site (Administrative Tools -> IIS Manager -> Websites) for that specific IP. This will leave the localhost (127.0.0.1) port 80 unbinded by IIS. User will have to restart the IIS service after this change has been made.
For Skype, the solution is easy. You can configure Skype (Tools->Option->Connection) to not use Port 80 as an alternative port.