According to the changelog, that has been resolved in 4.6.9:
"Fixed an issue with the Archive page being redirected to an incorrect URL on sites set up on a subfolder, with the language URL option set to “Default language in directory”"
I would like to point out that this site has been running happily for over a year now, before 4.6.8. Obviously, we haven't been able to maintain the site properly for a while now.
Welcome to WPML support. I'd be happy to help you with this.
I just tested on a fresh install on my local host and can't replicate the issue with WPML 4.6.9.
So, To debug this issue further, I would need to check your site settings once, for this I would need temporary access (wp-admin and ftp) to your site.
So could you please provide me with those details, you will find the needed fields for this below the comment area when you log in to leave your next reply. hidden link