Are your accounts older accounts that haven't been used for a while? Mine is, so I figured I'd just start over and create a new account.
I created the new account and just to test I reset the password and got the e-mail confirmation almost instantly. So I figured, ok, I'll just scrap the old account (the one that I can't reset the password on) and start with this new one. I loaded SWG and was subscribing with the new account, but it won't let me because that cd-key is already in use. So apparently, everything about my original account is still stored, but something is stopping it from sending the e-mail with the reset password...
And yes, it is kind of stupid to have a link to get help on password recovery when you have to log in to get it.
Anyways, let me know how it works out for you and I'll do the same.