Objection 1. It would seem that the Godhead was separated from the flesh when Christ died. For as Matthew relates (27:46), when our Lord was hanging upon the cross He cried out: "My God, My God, why hast Thou forsaken Me?" which words Ambrose, commenting on Luke 23:46, explains as follows: "The man cried out when about to expire by being severed from the Godhead; for since the Godhead is immune from death, assuredly death could not be there, except life departed, for the Godhead is life." And so it seems that when Christ died, the Godhead was separated from His flesh.
Objection 2. Further, extremes are severed when the mean is removed. But the soul was the mean through which the Godhead was united with the flesh, as stated above (Question 6, Article 1). Therefore since the soul was severed from the flesh by death, it seems that, in consequence, His Godhead was also separated from it.
Objection 3. Further, God's life-giving power is greater than that of the soul. But the body could not die unless the soul quitted it. Therefore, much less could it die unless the Godhead departed.
On the contrary, As stated above (16, 4,5), the attributes of human nature are predicated of the Son of God only by reason of the union. But what belongs to the body of Christ after death is predicated of the Son of God--namely, being buried: as is evident from the Creed, in which it is said that the Son of God "was conceived and born of a Virgin, suffered, died, and was buried." Therefore Christ's Godhead was not separated from the flesh when He died.
I answer that, What is bestowed through God's grace is never withdrawn except through fault. Hence it is written (Romans 11:29): "The gifts and the calling of God are without repentance." But the grace of union whereby the Godhead was united to the flesh in Christ's Person, is greater than the grace of adoption whereby others are sanctified: also it is more enduring of itself, because this grace is ordained for personal union, whereas the grace of adoption is referred to a certain affective union. And yet we see that the grace of adoption is never lost without fault. Since, then there was no sin in Christ, it was impossible for the union of the Godhead with the flesh to be dissolved. Consequently, as before death Christ's flesh was united personally and hypostatically with the Word of God, it remained so after His death, so that the hypostasis of the Word of God was not different from that of Christ's flesh after death, as Damascene says (De Fide Orth. iii).
Reply to Objection 1. Such forsaking is not to be referred to the dissolving of the personal union, but to this, that God the Father gave Him up to the Passion: hence there "to forsake" means simply not to protect from persecutors. or else He says there that He is forsaken, with reference to the prayer He had made: "Father, if it be possible, let this chalice pass away from Me," as Augustine explains it (De Gratia Novi Test.).
Reply to Objection 2. The Word of God is said to be united with the flesh through the medium of the soul, inasmuch as it is through the soul that the flesh belongs to human nature, which the Son of God intended to assume; but not as though the soul were the medium linking them together. But it is due to the soul that the flesh is human even after the soul has been separated from it--namely, inasmuch as by God's ordinance there remains in the dead flesh a certain relation to the resurrection. And therefore the union of the Godhead with the flesh is not taken away.
Reply to Objection 3. The soul formally possesses the life-giving energy, and therefore, while it is present, and united formally, the body must necessarily be a living one, whereas the Godhead has not the life-giving energy formally, but effectively; because It cannot be the form of the body: and therefore it is not necessary for the flesh to be living while the union of the Godhead with the flesh remains, since God does not act of necessity, but of His own will.
Source: Summa Theologica (New Advent)