obstinate - persist stubbornly; "he obstinates himself against all rational arguments"

ask for it, ask for trouble - persist with actions or an attitude despite the probability that it will cause trouble; "He is asking for trouble with his behavior"

plug, plug away - persist in working hard; "Students must plug away at this problem"

stick with, stick to, follow - keep to; "Stick to your principles"; "stick to the diet"

preserve, uphold, carry on, continue, bear on - keep or maintain in unaltered condition; cause to remain or last; "preserve the peace in the family"; "continue the family tradition"; "Carry on the old traditions"