Account Auto-Locking on Supsicious Activity

Now while I like to think I run a pretty secure computer, I know that a computer that is completely safe and invulnerable to attack while connected to the internet is an illusion.

That being said, is the fact that my ISP keeps changing my IP address whenever I reboot the modem causing this auto lock-down of my account to occur?

Yes, your IP changing is why SE's system is doing this. Allegedly if you get yourself a Security Token SE will stop doing this, however I've seen some assert this isn't always going to stop it.

Thank you.

If you got smartphone (iOS or Android), you can SquareEnix Software Token free, instead of the hardware one.