Just want to post about this and add to the collective information on the internet about issues with accessing Southwest.com while overseas. In my case, while in China, I get the following error when accessing https://www.southwest.com .
I tried using a VPN service, but that too failed. One possible solution from googling suggests using the Southwest app or using the mobile version of the website at https://mobile.southwest.com . As of today (20161130), I can confirm able to accessing the mobile version of the website. I did not try to log in and buy tickets, however.
From my fuzzy recollection, this issue has been ongoing for a few months. One commenter (caat0369) at https://www.tripadvisor.com/ShowTopic-g1-i10702-k9513330-o60-Problems_accessing_Southwest_com-Air_Travel.html goes so far as to claim that this is done intentionally on the part of Southwest.