Quote Originally Posted by worldofneil View Post
It's probably because the launcher is actually a web page and is using Internet Explorer to save the username (in a cookie). Since Windows 10 replaced IE with their new Edge browser, it's still compatible enough to render/display, but apparently not to save the details.
This is false, Internet Explorer still exists in Windows 10. It's security settings that sometimes stop it saving - it happened on one of my updated computers but not the other.

Solution -
Just found a solution! Perform the following steps:
1.Hit windowskey-s to open the windows search.
2.Type in "Internet Options" and select the top result which opens the Internet Properties window from the control panel.
3.Click the Security tab.
4.Click the "Trusted Sites" zone.
5.Click the "Sites" button.
6.Add both https://square-enix.com and http://square-enix.com to the list of trusted sites.
7.Apply/close out of the Internet Properties window.
8.Relauch the launcher and check the "Remember Square Enix ID" button and login.
9.Success!