Perhaps he has lost too many people close to him. If his friends, like Annabeth or Grover, were to die in a particularly tragic way, he could be so grief - stricken that he no longer wants to live in a world without them. He might think that death is the only way to escape the pain of their loss.
Another reason could be disillusionment with the gods. If he realizes that the gods are not as just or benevolent as he once thought, and that his efforts in serving them and saving the world are in vain, he might choose to ask for death. He could feel that there is no point in continuing to live in a world ruled by such flawed deities.