The antonyms for the word "give up on" are many: keep trying, endure, persevere, persist, hold on, hold out, push on, strive, fight, carry on, never give up, maintain hope, stay the course, stand firm, refuse to quit, and many more. Giving up on something or someone can be tempting when the going gets tough, but it is important to remember that perseverance pays off in the end, and success often comes to those who refuse to quit. So, if you are feeling discouraged, remember that there are many ways to say "never give up," and that each one can help you stay focused on your goals and dreams.