You need to change your POL password through the Square Enix Management Account System website -
https://secure.square-enix.com/account/ - not through your POL viewer.
Go to the site, log in, on the left hand side click 'Select Service', then on the right hand side click 'Final Fantasy XI'.
Then, when it appears, click 'Options List', scroll to the bottom of the following page and click on the update button that is shown to the right of the 'Update PlayOnline Password' text.
Change your password.
I hope that that works for you - please come back and post what happens!