You can append a random variable to the URL. But first a quick primer on URLs:
"http://" is the protocol
"www.example.com" is the host name (the computer the web page is on)
"/some/place.html" is the path
"?random=SomeRandomValue" is the query string
The query string is a question mark (?) followed by a set of "variable=value"s, separated by ampersands (&). So if your URL is http://www.a.com/b.html you could make it http://www.a.com/b.html?rand=1234. If your original URL already had a query string (e.g. http://www.a.com/b.html?a=1) then you'd use http://www.a.com/b.h...?a=1&rand=1234. That will force the page to reload because the browser recognizes that could be a different page.. Just remember to use a different random each time.
That's a common problem in a number of programming situations not just limited to LabVIEW. The HTTP protocol has metadata saying how long to keep a cached copy around and also metadata to say if a file is newer than another copy. I'm not sure if your web server isn't sending that data, it's sending the wrong data, or LabVIEW isn't respecting that.