According to Classical mythology, they're immortal beings and cannot die. I checked _The Dictionary of Greek and Roman Biography and Mythology, Volume 3_, and also the website below (an excellent resource), and neither mention any weakness, or that they died or were killed.
Perhaps Dawn (Aurora or Eos) could be a sort of enemy? The Greeks and Romans were always adding to and rewriting their own myths, so go for it!
I *think*, though, that if you kill them off, your story will have to explain dreams -- or why, in your story, we no longer have them.