Restore Things to iPhone from iTunes
If you're absolutely sure that you have SYnced the phone and the app is still not there, you can try to remove it from iTunes too. Then you go to the App Store (make sure you are logged with the SAME account you were when you bought it for the first time) and buy it again, the store will inform you that it's "a free upgrade" and will re-download it. It will not charge you again.