I am a semi-finalist this year after being rejected the first time I applied two years ago. Reapplying with a stronger application makes a lot of sense, and I know a lot of people who didn't get it the first time (or second time, for some) but then were accepted and said that it was all worth it. I think that if you spent enough time working on your application this year, then half of the work is done for you to reapply. Speak with some faculty advisors, or even the Fulbright committee on your campus, and see where the weak parts of your application were. Then, spend time strengthening it so when you reapply youre a more competitive applicant.
One thing I would strongly advise to many people who are applying is to make sure that Fulbright isn't the only thing you are working on: you can always defer grad programs, but you can't defer Fulbright. And if you don't get accepted into Fulbright, and haven't applied to grad schools, then you're left with having to find something else to work on for at least another year.
I would say don't take the GRE if you haven't studied for it.