die out        
phrasal verb with die verb [ I ] uk/daɪ/ us/daɪ/  dying | died
B2 逐渐消失;灭绝
to become less common and finally stop existing
  Dinosaurs died out millions of years ago. 数百万年前恐龙就已经灭绝了。 
 It's a custom that is beginning to die out. 这是一种正在消失的习俗。