Antonym of PERSISTENT

Persistent : continuing firmly or obstinately in an opinion or course of action in spite of difficulty or opposition.
Wavering : moving in a quivering way; flickering.
Obstinate : stubbornly refusing to change one's opinion or chosen course of action, despite attempts to persuade one to do so.
Enduring : lasting over a period of time; durable.
Steady : firmly fixed, supported, or balanced; not shaking or moving.

Antonym of Persistent is Wavering