Dale Carnegie's book "How to Win Friends and Influence People" is a great read and surprisingly filled with stories about persistence. Here's one I enjoyed.
"In the early nineteenth century, a young man in London aspired to be a writer. But everything seemed to be against him. He had never been able to attend school more than four years. His father had been flung in jail because he couldn’t pay his debts, and this young man often knew the pangs of hunger. Finally, he got a job pasting labels on bottles of blacking in a rat-infested warehouse, and he slept at night in a dismal attic room with two other boys - guttersnipes from the slums of London. He had so little confidence in his ability to write that he sneaked out and mailed his first manuscript in the dead of night so nobody would laugh at him. Story after story was refused. Finally the great day came when one was accepted. True, he wasn’t paid a shilling for it, but one editor had praised him. One editor had given him recognition. He was so thrilled that he wandered aimlessly around the streets with tears rolling down his cheeks.
The praise, the recognition, that he received through getting one story in print, changed his whole life, for if it hadn’t been for that encouragement, he might have spent his entire life working in rat-infested factories. You may have heard of that boy."
I'm not sure I know anyone who has failed at what they wanted to accomplish if they just kept persisting. But I know plenty who have given up after a try or two. And sometimes unfortunately it's going to take 34 or more tries.