Is your URL really "http" rather than "https"?
Can you duplicate the same failure with a publicly visible URL (so that it a debugger can be attached to watch it fail)?
Unfortunately, no - this is a commercial product.
Does reverting to git-client-plugin 1.6.3 work for you?
Yes. Git plugin at 2.0.4 is Ok.
Are there any other hints you can offer which might suggest how your installation is different than the installations which are working with git-client-plugin 1.6.4?
I'm using 'Credentials' - there probably aren't that many Auth + non-HTTPS set-ups out there.
I'll try running a trace on the git conversation next to see if that yields anything interesting.