Hi team,
I noticed the same problem here 
Domain : PushingBox.com
Server IP : 213.186.33.19
I’m using the TwitterOAuth library from @abraham (https://github.com/abraham/twitteroauth)
and get a HTTP error code 0 when trying to reach api.twitter.com
But Twitter said this about the error code 0 (https://dev.twitter.com/docs/faq#6870) :
If you’re making requests to the Twitter platform and receive an HTTP status code “0,” it means that the request never made it to our servers. Investigate whether your HTTP library, programming language, system environment, network and/or proxies are configured to allow traffic over HTTP and HTTPS to the endpoints you will be using.
So, I think the problem is on the server side…
Thanks,
Clement