Objection 1. It would seem that this sacrament should be given in any kind of sickness. For no kind of sickness is determined in the fifth chapter of James where this sacrament is delivered to us. Therefore this sacrament should be given in all kinds of sickness.
Objection 2. Further, the more excellent a remedy is, the more generally should it be available. Now this sacrament is more excellent than bodily medicine. Since then bodily medicine is given to all manner of sick persons, it seems that this sacrament should be given in like manner to all.
On the contrary, This sacrament is called by all Extreme Unction. Now it is not every sickness that brings man to the extremity of his life, since some ailments prolong life, according to the Philosopher (De Long. et Brev. Vitae i). Therefore this sacrament should not be given in every case of sickness.
I answer that, This sacrament is the last remedy that the Church can give, since it is an immediate preparation for glory. Therefore it ought to be given to those only, who are so sick as to be in a state of departure from this life, through their sickness being of such a nature as to cause death, the danger of which is to be feared.
Reply to Objection 1. Any sickness can cause death, if it be aggravated. Hence if we consider the different kinds of disease, there is none in which this sacrament cannot be given; and for this reason the apostle does not determine any particular one. But if we consider the degree and the stage of the complaint, this sacrament should not be given to every sick person.
Reply to Objection 2. The principal effect of bodily medicine is bodily health, which all sick people lack, whatever be the stage of their sickness. But the principal effect of this sacrament is that immunity from disorder which is needed by those who are taking their departure from this life and setting out for the life of glory. Hence the comparison fails.
Source: Summa Theologica (New Advent)