9 out of 10 times it really is the Akamai firewall. Usually you will be removed from their blacklist automatically after awhile.
The only way to make sure is to run cURL from SSH so you can see the full output, that will in this case mention that the request is blocked by Akamai.
The reason for being blocked can be another user of the same hosting provider you are using, as in most cases you will share your hosting IP with a number of websites.
The other 1 out of 10 times it is any other network issue between apache – php – curl – openssl – hosting firewall and routing / proxies. That too will usually be indicated in the verbose cURL output (the SSH command).
I suspect MailChimp / Akamai runs some sort of “autoban” script periodically, as we usually get multiple reports at once about Akamai blockades.
To confirm that it is not a problem with the API key itself, you can just type the URL in your browser:
https://us1.api.mailchimp.com/3.0/?apikey=test
Replace us1 with the characters in the end or your API key, after the minus sign.
Replace test with everything in front of the minus sign of your API key.
If everything works well you should see a lot of data from your account. If you get an error when trying this from your own browser that would indicate there is an issue with your API key and generating a new key will usually solve the issue.
Please keep in mind that your API key gives full access to your MailChimp account, so take care of your browser history or use incognito mode!
Hope that helps,