Think I have to agree about someone, something trying to steal your password. Don't do it through that popup. It's different when logging out and back in on WGT, that is to their servers and your account. By looking at the date of your account, I am betting this is happening on a mobile account. There was something recently IIRC about mobile passwords being hacked, and also IIRC it was advised to change your password.
It's also not strange that you can't reuse an old password. Never tried it here, but a number of places will NOT let you use an old password.