I can see update requests coming from your website and seem to be processed fine. At least Secure Downloads addon requested update today at approx. 10 AM UTC.
It might be the case when your server cannot access update server for some reason. But this should be definitely recorded in PHP error logs. Strange thing it’s not there.
Anyway, I will try to add reasonable timeout for updates checking. If error occurs during the process, it won’t stall WP admin area at least.