error: An Unexpected HTTP Error occurred during the API request

I had the same problem before. When I asked my friend, who is maintaining the server, he answered me that it’s because of the server firewall. When he turned of the firewall, everything was ok (plugins can update, akismet can check for spam, etc.).

So, if you’ve checked all your settings with Core Control (make sure that all the tranports are turned on) and the problem still happens, you should ask your host provider for the firewall settings, just like me.

Hope that helps.