All Elder Dragon monsters.
After fighting for 25 minutes with some Elder Dragons (those who have wings, Jhen Mohran and Ceadeus) and it hasn't died, it will flee by flying away. This is called repelling a monster. Instead of slaying it, you will complete the quest, but it won't count towards a slay and you will not get a money reward. But the next time you fight that monster, it will be the same. For example, if you cut off the tail or break Kushala Daora's horns, next time you try to kill it, it will be same enemy, without his tail and horns, but it will recover some of its health (as long as its the same rank).