I actually had that happen before to me in the past as well, where I just left the login launcher in the background while I alt-tabbed to check out websites. And it automatically logged me in after a looooong time on its own lol. It's just weird though because I've had Windows 10 upgraded since last summer and the launcher worked fine up until recently. I'm guessing it's probably some new Windows 10 update that's causing this (as I can log into FFXIV right away when I fire it up on my playstation 4).

Ah well, it's good to know I'm not the only one with this issue though - as much as it sucks lol. Here's hoping the next Windows 10 update or whatever fixes the issue for us