"Q. How many times can I take the AFOQT?
A. You can take the AFOQT two times with a minimum interval of six months between taking them. Waivers to take the test a third time are granted to people who have completed significant training since the last time they took the test if the training impacts the skills being measured (college-level math and English courses, private pilot’s license, etc.). If you inquire on a score and see blanks in the area where the scores should be, it’s usually because the person took the test a third time without authorization."
I don't know the process of getting a waiver to take it a third time or how often one is approved.