Although they can be used in a vaguely positive lighting, persistent, stubborn, and obstinate are negative connotation words.
Persistent - continuing firmly in a course of action in spite of difficulty or opposition
Stubborn - having or showing determination not to change one's attitude or position on something, usually in spite of good arguments or reasons to do so
Obstinate - stubbornly refusing to change one's opinion or chosen course of action despite attempts to persuade one to do so
