persevere

To persist steadfastly in pursuit of an undertaking, task, journey, or goal, even if hindered by distraction, difficulty, obstacles, or discouragement.

I will persevere in my course of loyalty, though the conflict be sore between that and my blood.

Sir Walter had sought the acquaintance, and though his overtures had not been met with any warmth, he had persevered in seeking it.

To stay constant; to continue in a certain state; to remain.