Wow, this thread really hit close to home as I've also had my keyring token since XI and I've been wondering how much battery life is left. In recent months I've noticed I'd need to press the button a bit harder to get the one-time password to appear- so I feel like it might've been near it's time. I wasn't aware if it just "dies out" or you get a warning on the screen, so just to be safe I immediately just deactivated that one (RIP) and registered the unused one from ARR's CE. To be honest, I read about the emergency password but had no idea that it wasn't for the keyring token- I had been putting off acquiring it thinking I still had time. Now I see it wasn't even relevant for me.

ANYWAY, I read this on the service agreement for registering the new one:

If you have a Physical Security Token and it runs out of batteries, it shall no longer obtain a one-time password and, consequently, you may be unable to log in to your Square Enix Account and the Services. Accordingly, if you have a Physical Security Token and the Physical Security Token indicates that its batteries are running low, you should immediately disable your Security Token registration or obtain a new Security Token.

In the event that your Security Token runs out of batteries, malfunctions, or becomes otherwise inaccessible or unusable, please contact the Square Enix Support Center for further assistance.
So, there must be a low battery warning? I didn't know about that (damn, I probably could've still got some more use out of the old one). Has anyone seen what it looks like? This is all I can share to be of help.

-Oh, and there was this, so the battery removal thing being a no-no is legit:

The following acts are prohibited:

(b) replacing the batteries of the Physical Security Token;