I have actually had coupon codes not be accepted at time of on-line reservations due to black-out, holidays, etc. In otherwords it gave me an error message and wouldn't let me proceed to make the reservation with that coupon code on it. If you don't get any errors and the coupon code shows up on your confirmed reservation you should be fine. I usually try and have printouts of the information with any "electronic" coupons with me(as well as a printout of the reservation with the rate on it in case of dispute.) Never had problems with paper coupons (which most of mine have been.)
Once there was this coupon code advertised on the AVIS website for a free weekend day just enter the code on your reservation. It was something like TUNA001. My receipt didn't show teh discount upon return and the agent gave me a little trouble because I didn't have a paper coupon. I ended up getting it though.
Recently at MSY they wanted me to sign the paper coupon which I thought was a little odd. She said so it couldn't be used again. She was collecting it so I don't know how it could be used again anyway. It's a bit of a pain to present a coupon if you are Preferred but I have never been denied the discount if it was on the reservation.