Final answer:
The most likely cause of the persistent infection with negative culture results on artificial media is Chlamydia trachomatis, an intracellular pathogen that does not grow on artificial media.
Step-by-step explanation:
The organism that does not grow on artificial media and is most likely to be the cause of the positive initial culture for penicillin-susceptible gonococci and the subsequent negative culture could be Chlamydia trachomatis. C. trachomatis is a difficult-to-stain, gram-negative bacterium and an intracellular pathogen, which causes the most frequently reported STI in the United States, chlamydia. Since intracellular pathogens like C. trachomatis require living cells to grow, they will not cultivate on artificial media commonly used in a lab setting, which explains the negative results in the subsequent test for the student's persistent infection.