When you've exhausted your own strength and feel like giving up, that's where real persistence begins. The speaker argues that recognizing your need for God and stepping into divine strength is how you keep moving forward instead of quitting.
Persistence doesn't even begin until you feel like giving up. After you've exhausted all of your ability, after you've come to the end of yourself and you recognize your need for God and you recognize it can only be him, that's when persistence comes in because you've moved beyond your own strength and you've now stepped into his. So don't give up, keep going.
