Rapture showed me a bug in Windows 7 (and maybe other versions) where reusing the name of an Internet shortcut (*.url file) can cause it to point to the old location instead of the new one. To reproduce this (in any browser), open two different Web pages that have the same page title; drag the first to the desktop to create a *.url shortcut; rename it; then drag the second in the same way. The resulting shortcuts will not point where you would expect, due to caching.
I have no idea how to clear the internal cache that causes the problem, and it doesn't sound like a good idea anyway.
Here is a quick workaround. Run the program below. You won't see anything, but while it is running, you can press Ctrl+Alt+C to create an Internet shortcut on the desktop that points to the URL that was on the Clipboard. (If there isn't a URL on the Clipboard, it won't do anything.)
In most browsers, you can easily use it by pressing Ctrl+L (focus address bar), Ctrl+C (copy address), Ctrl+Alt+C (create the desktop shortcut).
Filenames are randomly generated because we can't see the page title, only the URL on the Clipboard. And if you want it to work all the time, then obviously you should configure it to run at startup.
Download UrlGrab and its source code.