What's the time period here?
Remember, Einstein once said that insanity is doing the same thing over and over and expecting different results.
Make sure you have improved your resume, networked, and fixed the issues with your first round.
Generally, if you recruit via channel x for role x, but then your situation changes (like graduation) you can then recruit via channel y for role y, even within the ban period.
Good luck on your 2nd attempt!