It seems to do this no matter when I enter a coupon code. If it's entered (which by the way, it still won't work with the button - I have to enter it and hit [enter] for the coupon code to work) -- I can clear my cart, add a different item to the cart, and the discount shows up again without me entering any code.
EDIT: I got the button to work. It had to be "submit" type. In your video tutorial, it says it should be type="button". When I switched it to submit, it works fine now.
Regarding the discount showing up - the only way I can get rid of it is by clearing my cookies. Is it supposed to act like this?