This issue usually happens when your hosting server is not receiving anything back from the calls towards Rey’s API server. This could happen either because Rey’s API server or your server rejects these remote calls in their firewalls.
First thing you should try is to contact your hosting support and ask them to verify if there is a restriction for sending API calls to https://api.reytheme.com/ , and if so, to whitelist it.
Just to double check, if you’re using Cloudflare, try to temporarily disable it and check if you can then make the API calls. Also, try to check if you can whitelist https://api.reytheme.com/ inside Cloudflare.
If this is not the case, it means Rey’s API server has blacklisted your server’s IP. In this case, please submit a new support request and let me know when this issue is happening. Also don’t forget to send your website URL and the administrator login details (or better, create a temporary new account for me ). It would be absolutely great if you can find out what’s your server ID address. I will basically just contact my hosting provider to ask them to whitelist this IP. Thanks!