Why should Christians strive to live long lives? At what lengths should they go to do so?

I understand that we are called to spread the gospel, but why should we (or should we at all) cling to physical life with white knuckles? I have known believers to go to extreme lengths to prolong their lives in the face of a terminal illness. During such an unfortunate occurrence would it not be a better witness to our faith to peacefully get your affairs together, spend time with loved ones while expressing your joy in your hope to be with Christ soon? Also, as medical tech advances at an amazing pace will there ever be a point in which it is imperative for a Christian to turn down life extending technology if it makes death a rare occurrence? (Think all genetic disease cured, cancer cured, worn out organs replaced with organs grown from your own stem cells. All of which might not be so far fetched in the next few decades.)