?
I don't think you're doing anything wrong, but based on this, and your previous error... it sounds like you've got some server/network oddities. That could be any one of a THOUSAND things, but it's definitely not ProGet nor the NuGet clients.
So, I'd suggest to put some wireshark or fiddler monitoring in between to see exactly what's happening, where they are coming from, and what the actual responses are.