I have been having this problem for a few months now. Someone in this thread hit the nail on the head: southwest.com isn't undergoing any long term maintenance, but they blacklist certain ranges of IP addresses for some reason. If you are trying to access the site from any of their blacklisted IP ranges, you get the message about undergoing maintenance. The only way around this is to use an entirely different internet connection, or find the people in IT security at SWA that maintain this blacklist.
Having the blacklist that isn't known by support personnel is one problem, but the bigger problem is that there is no indication that the problem logging on is due to being on a blacklist. Because the message is about maintenance, the support troubleshoots it like it's a maintenance window problem. When they eliminate any actual maintenance window as being the culprit, they just shrug and say it must be the customer's problem. After all, they won't be able to replicate the issue if they aren't attempting to access the site from a blacklisted IP address.
I occasionally access the internet via Amazon's AWS cloud (there are a ton of businesses who do this same thing). Because Amazon's cloud is used by a wide range of people and organizations for a wide range of things, some of the activities being performed in AWS have led to the entire range of AWS addresses being put on blacklists. I can't get to lowes.com or homedepot.com at all. Those sites, at least, give a message the indicates that the reason I can't get there is because my IP isn't allowed. Southwest lets you browse the site, but just won't allow you to log in. The message is very misleading, and the fact that nobody at SWA seems to realize that the problem is being on a blacklist means that you can't ever make the case to have your IP taken off the blacklist. Super frustrating. This needs to be addressed.
