So, I called Emirates and they mentioned again that they are not aware of this. They did mention a lot of failed update logs on my PNR for that. The associate took a guess and said perhaps this is because my first flight is not EK. Not sure what that meant. In any case, she took care of the information over the phone.

later I was able to modify my information on that website using IE8. In any case, there is definitely a problem with that page and I hope they fix it.