I used to use Bugzilla just fine, but the last few times that I have used it, it no longer stores my login credential properly. I have to re-login three time during the course of adding a new bug. Before it would know who I was right when I connected to bugzilla.redhat.com/bugzilla I am using Mozilla 2001011204 (the sam eon for the last month, it was working properly with this verison of Mozilla before) on Windows 98SE. I have not diabled Cookies or Javascript.
Please use the Mozilla cookies editor and remove the cookies pertaining to bugzilla.redhat.com. Then relogin to Bugzilla and see if the problem goes away. Tasks->Privacy and Security->Cookie Manager->View Stored Cookies
Works correctly after removing all cookies for bugzilla.redhat.com, and re-logging in.