It is basically a browser message that connectivity was lost during the download of the page. There's a recently discovered issue with encryption support--enable them under the advanced settings for your browser/internet. Even if you have blocked IE through WinSxS, it's settings are still in play with the launcher, since it is built on MSIE. You can still get at it through the Internet Options snap-in in Control Panel (or running inetcpl.cpl from the run/search box). It's under the Advanced tab, scroll down to the bottom of the list. Last week, SE put a notice up about a recent Windows Update that is resetting the options and causing issues, but it isn't necessarily limited to IE 11:

http://na.finalfantasyxiv.com/lodest...1acf43974ec41d
04/17/2015 4:30 AM
Login Issue (Apr. 17)
Currently, we are receiving contacts from users in certain environments who have become unable to log in to services connected to their Square Enix Account.

Investigation has revealed that the issue stems from application of the latest Windows Update, which turns off the “Use SSL 3.0” setting under Internet Options in Internet Explorer 11.

We ask that users who are experiencing this issue take the following steps to change their Internet Explorer 11 settings.

[Steps]
1. Open Internet Explorer 11
2. Open Internet Options
3. Select the “Advanced” tab
4. Check the boxes next to the following and click “Apply”:
- Use TLS 1.0
- Use TLS 1.1
- Use TLS 1.2

[Affected Services]
- FINAL FANTASY XIV: A Realm Reborn
- The Lodestone
- Mog Station
- FINAL FANTASY XIV Forums
- Square Enix Account Management System