PERSEVERE
verb
verb
continue in a course of action even in the face of difficulty or with little or no indication of success.
"his family persevered with his treatment"
persist, continue, carry on, go on, keep on, keep going, not give up, struggle on, hammer away, be persistent, be determined, see/follow something through, keep at it, show determination, press on/ahead, stay with something, not take no for an answer, be tenacious, be pertinacious, be patient, stand one's ground, stand fast/firm, hold on, hold out, go the distance, stay the course, plod on, plough on, grind away, stop at nothing, leave no stone unturned, informal soldier on, hang on, plug away, peg away, stick to one's guns, stick at it, stick it out, hang in there, bash on
"she always perseveres in spite of discouraging setbacks"