I would think that perserverance becomes cluelessness if there is no meaningful improvement in the applicant between cycles. The lazy pre-med that thinks "I didn't get in this year, but if I reapply next year they will think I'm really serious and they'll let me in" and then doesn't do anything is the clueless one.
For instance, take these two hypotheticals, both initially equal, subpar "stats."
Pre-Med #1: Applied once, got rejected, lived at home and did a week or two of shadowing, applied again, got rejected, wash, rinse, repeated, reapplied, ???
Pre-Med #2: Applied once, got rejected, obtained EMT certification and did a few weeks of shadowing, reapplied, rejected. Obtained advanced EMT certification, retook classes, improved GPA, improved MCAT, better rec letters, reapplied, and ???
This isn't to say that Pre-Med #2 might still never get in, but his app would be given a more serious look.