Hi Tolga,
If I understand correctly, you've registered your custom domain, and setup the appropriate SSL Cert for the domain (instead of SSH key?) on your App Engine app (however, it shows there is no SSL cert when going to your custom domain). Do you see incoming request from the IPs of Vodafone at logging section of your app? Also I'll need you to clarify that if it always gives "request time out" using *.
appspot.com to your app while we can confirm that your custom domain is always resulting "request time out".
Please notice that "request time out" normally indicates that no echo reply messages were received within the default time, and can be due to many different causes, which can include network congestion, failure of the ARP request, packet filtering, routing error or a silent discard.
- Jun