Version:           4.2.90 (KDE 4.2.90 (KDE 4.3 Beta2)) (using 4.2.90 (KDE 4.2.90 (KDE 4.3 Beta2)), 4.2.90-1.fc11 Fedora)
Compiler:          gcc
OS:                Linux (x86_64) release 2.6.29.5-191.fc11.x86_64

This TCP conversation:

GET /login.php HTTP/1.1
Host: mysite.rudd-o.com
Connection: Keep-Alive
User-Agent: Mozilla/5.0 (compatible; Konqueror/4.2; Linux 2.6.29.5-191.fc11.x86_64; X11; x86_64; es, en-US, en) KHTML/4.2.90 (like Gecko) Fedora/4.2.90-1.fc11
Accept: text/html, image/jpeg;q=0.9, image/png;q=0.9, text/*;q=0.9, image/*;q=0.9, */*;q=0.8
Accept-Encoding: x-gzip, x-deflate, gzip, deflate
Accept-Charset: utf-8, utf-8;q=0.5, *;q=0.5
Accept-Language: es, en-US, en
Cookie: PHPSESSID=sqh58cf6o99ng4bjg2ajn6kkm6

HTTP/1.1 401 Unauthorized
Server: Apache/2.2.3 (CentOS)
X-Powered-By: PHP/5.1.6
WWW-Authenticate: Basic realm="Mysite"
Content-Type: text/html; charset=UTF-8
Content-Length: 0
Date: Tue, 30 Jun 2009 13:40:27 GMT
X-Varnish: 1787744650
Age: 0
Via: 1.1 varnish
Connection: keep-alive

--------------------------------

Results in an error message in Konqueror that says:

------------------------------

El archivo o carpeta no existe

Descripción:
El archivo o carpeta especificada /login.php no existe.

---------------------------------

Basically, when this site demands authentication, konqueror pathologically believes the uri does not exist.

This page in question works correctly with Firefox -- I am prompted for basic authentication and the site works fine.