If you leave a round in progress in Tiger Woods, you can not save your progress to that point. You have to complete the event in order to be prompted to save. It's kinda dumb the way it is set up, but it's the only way I've found to actually get things to save. On the plus side, if you're having a really bad round, quitting the round doesn't penalize you at all.
I'd recommend going through the Tiger Challenges to get used to the game play a bit.