If I remember correctly, you have to use it within 14 days. You have to go to a special Guest Services window before you leave the park and get the second day free added to it. It is not automatic - it has to be asked for.
It's actually second day within seven days. As we are usually in Orlando for seven nights/six days, we usually go to Sea World on day 1 and again on Day 6.
Thanks for asking/answering this! I am a SW Orlando newbie and haven't used the 2nd day option before so I didn't know you had to go have the second day added.