I’ve just read an interesting paper by Kirk Sanders in a new collection edited by him and Jeffrey Fish: ‘Philodemus and the fear of premature death’.  In part of the article, Sanders is interested in whether the Epicureans give a satisfactory response to the fear that one might die prematurely, before one’s life is complete. I discussed this a bit in my 2004 book (ch. 4) but I think there is a gathering consensus that Philodemus certainly did address this concern and may well have said something interesting about it.
I think there are two general questions here:
1. Did any Epicurean give an account of a complete life which shows that a person has a good reason to continue to live on once a complete life has been attained? What is that good reason?
2. If the Epicureans agree that there is a sense in which it might be bad to die prematurely (however they understood the notion of prematurity), would it not be correct for an Epicurean student therefore to be anxious about this prospect? But if the student is anxious, then he cannot attain ataraxia. And if he has not attained ataraxia then he will not live a complete life. Note that this is no mere empty fear; the student has a reason to fear premature death based on a correct understanding of what constitutes a good human life.
Regarding 1., Sanders has a persuasive case for saying that Philodemus, at least, thought we have reason to continue to live at least as long as it takes to become ataraxic, although he also perhaps thought that it was necessary in addition to live for at least some time in that state before a life could properly be called complete.
Sanders also has an interesting argument against the problem in 2.
‘In response, it should first be noted that Warren’s claim that premature death ‘is not to be feared if and only if one has attained ataraxia' is too strong. While it is true that premature death is only possible for one who has not yet attained ataraxia, not every possible evil is itself a reasonable object of fear. In order for a fear to be rational, it is required that one be justified in judging its object to be not only a genuine harm but also imminent’ (p. 231).
Since it is not the case that the young should think their death imminent they have no justified reason to fear premature death. And, Sanders suggests, this will be true for all but the very aged or infirm.
'Imminent' here does not mean 'impending' or 'near at hand'. If I know I will be struck down by an agonizing illness in forty years time I think I might reasonably fear that. (Sanders' example in the bit following the section I quoted concerns it being irrational to fear dying in a plane crash because such crashes are so infrequent). In that case, the important point is whether it is likely that a person will die in the period between the present and a later attainment of ataraxia. A young student worried that she is not yet ataraxic but might be struck down tomorrow in an accident will presumably be told that such an event is vanishingly unlikely. Yes, if that unlikely event does happen then her life will be incomplete and her death premature. So she should take care crossing the road and try not to get into dangerous situations. Fortunately, Epicureanism is something that you can work on at any time in your life. And if you’re smart then the Epicurean goal is something relatively quick to attain. This rather special fear of premature death, looked at from another perspective, is just one more reason to want to become a wise Epicurean.
 K. R. Sanders, 2011, ‘Philodemus and the fear of premature death’ in J. Fish and K. R. Sanders eds. Epicurus and the Epicurean Tradition, Cambridge: CUP, 211–34.