Objection 1. It would seem that the tree of life could not be the cause of immortality. For nothing can act beyond its own species; as an effect does not exceed its cause. But the tree of life was corruptible, otherwise it could not be taken as food; since food is changed into the substance of the thing nourished. Therefore the tree of life could not give incorruptibility or immortality.
Objection 2. Further, effects caused by the forces of plants and other natural agencies are natural. If therefore the tree of life caused immortality, this would have been natural immortality.
Objection 3. Further, this would seem to be reduced to the ancient fable, that the gods, by eating a certain food, became immortal; which the Philosopher ridicules (Metaph. iii, Did. ii, 4).
On the contrary, It is written (Genesis 3:22): "Lest perhaps he put forth his hand, and take of the tree of life, and eat, and live for ever." Further, Augustine says (QQ. Vet. et Nov. Test. qu. 19 [Work of an anonymous author, among the supposititious works of St. Augustine): "A taste of the tree of life warded off corruption of the body; and even after sin man would have remained immortal, had he been allowed to eat of the tree of life."
I answer that, The tree of life in a certain degree was the cause of immortality, but not absolutely. To understand this, we must observe that in the primitive state man possessed, for the preservation of life, two remedies, against two defects. One of these defects was the lost of humidity by the action of natural heat, which acts as the soul's instrument: as a remedy against such loss man was provided with food, taken from the other trees of paradise, as now we are provided with the food, which we take for the same purpose. The second defect, as the Philosopher says (De Gener. i, 5), arises from the fact that the humor which is caused from extraneous sources, being added to the humor already existing, lessens the specific active power: as water added to wine takes at first the taste of wine, then, as more water is added, the strength of the wine is diminished, till the wine becomes watery. In like manner, we may observe that at first the active force of the species is so strong that it is able to transform so much of the food as is required to replace the lost tissue, as well as what suffices for growth; later on, however, the assimilated food does not suffice for growth, but only replaces what is lost. Last of all, in old age, it does not suffice even for this purpose; whereupon the body declines, and finally dies from natural causes. Against this defect man was provided with a remedy in the tree of life; for its effect was to strengthen the force of the species against the weakness resulting from the admixture of extraneous nutriment. Wherefore Augustine says (De Civ. Dei xiv, 26): "Man had food to appease his hunger, drink to slake his thirst; and the tree of life to banish the breaking up of old age"; and (QQ. Vet. et Nov. Test. qu. 19 [Work of an anonymous author, among the supposititious works of St. Augustine) "The tree of life, like a drug, warded off all bodily corruption."
Yet it did not absolutely cause immortality; for neither was the soul's intrinsic power of preserving the body due to the tree of life, nor was it of such efficiency as to give the body a disposition to immortality, whereby it might become indissoluble; which is clear from the fact that every bodily power is finite; so the power of the tree of life could not go so far as to give the body the prerogative of living for an infinite time, but only for a definite time. For it is manifest that the greater a force is, the more durable is its effect; therefore, since the power of the tree of life was finite, man's life was to be preserved for a definite time by partaking of it once; and when that time had elapsed, man was to be either transferred to a spiritual life, or had need to eat once more of the tree of life.
From this the replies to the objections clearly appear. For the first proves that the tree of life did not absolutely cause immortality; while the others show that it caused incorruption by warding off corruption, according to the explanation above given.
Source: Summa Theologica (New Advent)