Are you prompted for FTP credentials when you upgrade WordPress currently?
No, I don't have provide my credentials.
How did you create the test install? Did you use SVN, or just download the beta zip file and extract it onto your server?
From a beta-zip file.
One simple way to determine this, is to run a manual update, you'll see it downloading the update from either "http://" or "https://", if it's the latter (https) then SSL works, if it's just http, SSL isn't able to work on your server, which is causing the issues.
The manual update downloads the update over https/SSL.
There's been a bunch of changes too, so try manually updating, and see if it updates to the latest nightly, and then see if automatic updates kick in..
I now manually updated to RC2, and will see if that fixes the problem. Is there a place where I can see when new builds come out?