I have been facing this for a long time since 3.5. something. Even after upgrading to 3.6 it continues. Firefox would keep on asking for proxy authentication even though i had given the id and password and even it remembers. But it will always ask for the id and password. Today looked around to find a solution, and i came across this, which seems to working. No popups for authentication for the past 2 or 3 hours. go to about:config and search and the following properties.
network.proxy.share_proxy_settings – FALSE
network.automatic-ntlm-auth.allow-proxies – FALSE
You can read the full discussion here
Setting these properties alone does not work. you have to set one more property.
network.auth.use-sspi – FALSE
These setting works in Flock & Thunderbird 3 also.