I hear 자꾸만 a lot in lyrical contexts like song or poetry lyrics, so it arouses some deeper emotions.
자꾸만 보고 싶은 사람 a person who I want to see over and over again
자꾸만 눈물 나요. Tears keeps coming out (of my eyes).
자꾸 열받게 하지 마세요. Stop annoying me.
강아지가 자꾸 짖어요. The puppy keeps barking.
자꾸 넘어져요. I keep falling down.