in reply to https through a proxy
But maybe I can offer some more clues. My home network consists of a Linux box that acts as a gateway and uses Squid. I have another Linux box and a Windows box that use the first as their gateway. I can successfully run Netscape and IE (respective boxes) via the proxy, but not Napster, and my inner Linux box experiences your exact same problem with LWP scripts that try to communicate throught the proxy.
I actually wrote a script once and had ybiC test it out for me. It failed on my box, but not his.
It has to be a Squid configuration problem, not LWP.