It really depends. If the ‘curl’ command was executed succesfully from the server that hosts your site I don’t know why it wouldn’t work from WordPress. If you don’t mind to give me ssh and wp-admin access, please send (temporary) credentials to admin at soft79.nl and I will take a look.
Alternatively you can disable auto updates from our plugin. Go to the settings page of our plugin, temporarily enable ‘debug mode’ and disable ‘auto update’.