Probably by design and i think it works like this (i don't know exactly how
this Authentix software works):

When you browse the unprotected files, there is no problem.
When you go to the protected folder, the server responses with a 401 asking
for authentication. The browser asks the user for credentials. Once this is
done, the browser has cached the credentials, and will not ask the the user
for the username and password anymore (but must still send them to the
server on each request). This works as long as the user navigates in the
protected folder, because the username and password can be matched on the
server.

But once the user navigates away from the protected folder, the browser will
continue to use the username and password supplied, and send it to the
server. Since the authentication is now handled by IIS, it notices that the
username and password is incorrect (there is no matching windows user), and
tells the browser that it will not accept the username and password it is
trying to use (authentication prompt shows).

So my guess is that the problem is "by design" because the browser tries to
be user friendly and "cache" the username and password, but don't understand
when to use it and when to not use it.

You can verify that my guess is correct by checking in the IIS log file. The
status codes gives you a great clue what is going on.

If you want your public folder to not ask for authentication, then
just configure IIS to only require Anonymous authentication for it.
IIS will never ask you for a password (when properly configured) no
matter what the client does.

Depending on how AuthentiX works, that protected directory may need
either Anonymous or Basic authentication enabled in IIS.

In general, having multiple authentication providers (i.e. both IIS
and AuthentiX) active in an URL namespace is dangerous and full of
such surprises. Almost all such surprises are either server
misconfiguration, bugs in the custom authentication provider, or user
misunderstanding of the authentication provider's capabilities.

//David
http://w3-4u.blogspot.com
http://blogs.msdn.com/David.Wang
//