Failed to connect to mandrillapp.com port 443: Connection timed out

I'm using Laravel 5.1. My web site sends e-mails using Mandrillapp's SMTP server. It works fine on my localhost/development.

But in my live server I get an PHP exception telling me that the connection has timed out:

ConnectException in RequestException.php line 49: cURL error 7: Failed to connect to mandrillapp.com port 443: Connection timed out.

Can anyone suggest a solution?

via Chebli Mohamed