That's the right way to try to update, but if the permissions on your filesystem aren't properly configured, the download can fail. You can try to change the permissions on your /tmp directory and see if that helps, but I can't give you recommendations on what needs to be fixed as every server configuration is different.
The other option is to download the full JFBConnect release package from the My Subscriptions area and simply re-install it through the Joomla installer. You don't need to uninstall first, and you won't loose any of your settings in the process.
Hope that helps!
Alex
Failed to update v4.2.5
