Christians are humans and humans do not like losing the things they've become attached to. Christian families especially tend to be very much attached to one another. Added to that is the human dread of death multiplied for loved ones. Throw into this the mix that they believe in a God who takes an intense interest in human affairs and you get Christian families praying for miracles rather than painless deaths.
A lot of Christians, and people in general, have are deeply confused by the fact that English only has one word for love. Love, in the Christian sense of the word, is desiring someone's ultimate good. Love, in the sense of human families, wants to protect the loved ones and keep them near. Storge, family love, wants to keep the suffering person with his or her family for as long as possible. Agape, Christian love, would realize that it is far better that they go on to Heaven than remain in agony in a world swiftly going to hell in a handbasket on well-greased wheels.