The conversion only happens if the linked URL and the text of the link are identical. In your example, since the http:// part isn't there, the text differs so the conversion won't be attempted. Try pasting URLs in and if there are specific cases there, let us know some further examples.
My local URL's do not convert to titles. I was having trouble with this right after the initial install and I added a line to .htaccess to allow local references. When that was not working consistently it was suggested that our firewall was causing a problem, So I added local references for our LAN to /etc/hosts.
Having different IPs for the domains locally is likely the problem. You will likely find that your webserver is either not listening on those IPs or if it is, it's not resolving your domain properly (because it's tied to a particular IP)
If you haven't, use the image proxy test in the control panel and that may give some details (though not the actual request body). This is for the image proxy so ideally test it with the URL to an image, but provided the domain is the same, this will likely give some useful details. Beyond that, you can use cURL/wget via the command line to request a URL that isn't loading what's expected to see what is loaded. You may need to make changes to your DNS or web server config to get this to work correctly.