Natural death, which results from illness or degenerative processes, is the antithesis of mercy killing. Even when life could be prolonged by medical treatment and is not, the death that may ensue is a death from the underlying illness, not a result of the withdrawal of care. The withholding of medical therapy is reasonable when the treatment is disproportionately burdensome (that is, the therapy - not the disease - is hard on the person) and relatively ineffective ("futile"). In other words, we are not ethically bound to use unwanted, non- beneficial therapies that serve to only prolong a person's dying. In fact, not doing so shows profound respect for the boundaries of natural life.
Read more at A Christian Response to Euthanasia