I always carry two - present one at check-in and then ask them to make me a photocopy for my records. That way they KNOW I still have a copy but, if for some reason they won't/can't, I still have my second copy. Can't be too careful when dotting "i's" and crossing "t's". You've got to document everything if you want to protect yourself.
I also call my elite reservations line the week before my stay to VERIFY my previous request for use of the EEO. This relieves my mind when they say, "yes, it's noted in your record."
Overkill, maybe....but the only one to suffer the consequences of something going wrong is me (I?). (Is there a grammatician out there who could tell me which is correct?)