Don't worry, it's not a true 'suspicious access' - all it is, is an IP block due to the fact you're accessing the game from another computer with a different IP address to the one you previously used, hence it's tricking SE's security system into thinking a hacker is possibly trying to access your account. This happens to me occasionally when my router is reset or my ISP reassigns us a new IP address after a few months.

Unfortunately there is no real way around it other than to use a Square Enix Security Token or Software Token which generates the one-time password that AngelMoon was referring to. Otherwise each time your IP address changes the IP block will kick in and you will need to change your password.