Persistence manifests itself in different ways. I know of two writers who got published with novel No 7. I also know that I would never have persisted that far. My form of persistence meant I was prepared to write and re-write repeatedly until I ended up with a publishing deal.
I persisted because...
a) I'd told myself that if I didn't write a novel in my MA year then I obviously didn't really want to write enough and should give it up. I have to admit that I got through all the taught modules of the MA without writing a word of my novel, only starting it in the last weeks of the course.
b) I'd got enough money to last two years. After that, it was the check out at Sainsburys. The thought of the checkout motivated me to write when I didn't feel like it, and to keep re-writing. I got my deal 1 year 11 months later.
c) I 100% believed that I was going to get published. I'm not sure how or why I believed that - there was no evidence back it up - but I did. It helped.
d) I was told it was very difficult to get published, which just made me even more determined to succeed.
Apart from a few lucky or well connected people, most writers have to persist to get published, and sometimes persist when all sane people would have given up and done something else. I don't know how you can make yourself keep on in the face of rejection, I just know it has to be done if you want to be published.