That may not be what you want, but it is the only guaranteed way to solve the problem. It's entirely up to the browser.
Cache management is also entirely up to the browser.
This should make sense if you remember that http is a stateless protocol. No state needs to be stored at the server. One kluge would be to code up a CGI script for your authorization that generates a slowly changing pseudo-random authorization realm string. You may want to cause the string to change for each form submission from a particular machine, as well as changing every 10 minutes or so. In essence, you are adding state to the server to outsmart the browser caches.