We have a very strange problem. We have a Windows Server 2003 box acting as a web server, mail server and an internal file server. The email client for the mail server runs through IIS on this box. At random periods during the day we can no longer access the email client user our external IP. We get a message saying the request timed out. At this point, remote desktop access to the server will no longer work either.
Internally, IIS appears fine as we can access it using the local name of the PC, and remote desktop connects using the local PC name as well, but we cannot access either using the external IP.
The really strange thing is that when we open a browser window on the server, we are able to access any pages on that server and it frees it up for anyone trying to access a page from outside our network. This also gets Remote Desktop working again.
So in other words, the fix is opening a browser window and typing in our external IP.