Man was created in the image of God (Genesis 1:26-27). All are still images of God (Acts 17:28), though the image has been marred such that one must be conformed to the image of Christ (Romans 8:29). Therefore, what man lost by virtue of the Fall cannot be an essential aspect of the imago Dei. If it were, men would no longer be the image of God.
Gordon Clark thought the essential property of the image of God is the innate faculty to reason. Man is by nature able to reason, and though this ability too has been dimmed due to sin, unregenerates with sufficient experience to occasion its use are nevertheless able to construct and understand propositions and even valid, if unsound, arguments:
The image must be reason because God is truth, and fellowship with him-a most important purpose in creation-requires thinking and understanding. Without reason man would doubtless glorify God as do the stars, stones, and animals; but he could not enjoy him forever. Even if in God’s providence animals survive death and adorn the heavenly realm, they cannot have what the Scripture calls eternal life because eternal life consists in knowing the only true God, and knowledge is an exercise of the mind or reason. Without reason there can be no morality or righteousness. These too require thought. Lacking these, animals are neither righteous nor sinful. (link)
There are some who have argued that man’s image must be understood with respect to his given tasks as well as the capacities used to fulfill said tasks (Genesis 1:28; link). However, I think this doesn’t work for a few reasons. Firstly, seemingly even on that view it is the last Adam rather than men who fulfills the stipulations of the Adamic covenant (see here and here). That being the case, if the or an essential feature of the image of God were functional, men would not and seemingly could not any longer image God. Secondly, considering Vos’ argument in Biblical Theology (pgs. 22-23) to the effect that if man’s function were an essential element in his makeup, he would have already known it, the fact Adam received special revelation explaining his function mitigates against the notion that it was essential to humanity:
The provision of this new, higher prospect for man was an act of condescension and high favour. God was in no wise bound on the principle of justice to extend [the covenant of works] to man, and we mean this denial not merely in the general sense in which we affirm that God owes nothing to man, but in the very specific sense that there was nothing in the nature of man nor of his creation, which by manner of implication could entitle man to such a favour from God. Had the original state of man involved any title to it, then the knowledge concerning it would probably have been formed part of man’s original endowment. But this not being so, no innate knowledge of its possibility could be expected. Yet the nature of an intensified and concentrated probation required that man should be made acquainted with the fact of the probation and its terms. Hence the necessity of a Special Revelation providing for this.
Does this mean fulfilling the Adamic covenant would have been by grace? No, for Adam's obedience to the dominion mandate in Genesis 1:28 and precept in Genesis 2:17 would have been the grounds for his inheritance. The point is that Adam's merit would have been pactum rather than condign. This is dissimilar to the covenant of grace in which our "personal obedience" is no longer the grounds for meriting our inheritance:
Man had been created perfectly good in a moral sense. And yet there was a sense in which he could be raised to a still higher level of perfection. On the surface this seems to involve a contradiction. It will be removed by closely marking the aspect in regard to which the advance was contemplated. The advance was meant to be from unconfirmed to confirmed goodness and blessedness; to the confirmed state in which these possessions could no longer be lost, a state in which man could no longer sin, and hence could no longer become subject to the consequences of sin. Man's original state was a state of indefinite probation: he remained in possession of what he had, so long as he did not commit sin, but it was not a state in which the continuance of his religious and moral status could be guaranteed him. In order to assure this for him, he had to be subjected to an intensified, concentrated probation, in which, if he remained standing, the status of probation would be forever left behind. The provision of this new, higher prospect for man was an act of condescension and high favour. (Biblical Theology pg. 22)
Thus, contrary to certain arguments against a Reformed anthropology, while there may be some similarity to Pelagianism in respect to one's personal obedience being the ground of fulfilling the Adamic covenant and inheriting eternal life, because Pelagians do not believe Adam was concreated morally upright, to argue against Reformed anthropology by alleging a correspondence between the two is specious.
Given the doctrine of original righteousness – that the moral character of man’s nature was indeed “very good” – the nature of what would have been merited by Adam is an interesting question. Is the implication that if he had completed the dominion mandate, then Adam would have merited eternal or, as Vos put it, “confirmed” life? It would appear that way, as Adam already possessed life, albeit mutably. The mutability of this life and the correlative righteousness mean that these too cannot be regarded as necessary to be in the image of God (although they may be necessary for healthily being in the image of God).
Aside from man’s rational faculty, one final common suggestion as to what distinguishes man as in God’s image is his [alleged] possession of “free will,” by which I mean not only the ability to choose – for Reformed Protestants believe men possess volitions – but also the ability to choose in such a way that it was not externally determined. Some Reformed Protestants think Adam possessed free will prior to the Fall, but it seems to me that there are at least two reasons why this can’t be the case:
1. Adam was originally righteous, so he could not have chosen to eat the apple according to his concreated “nature.” An inference one could draw from this would be that a precondition for Adam’s eating of the apple was the passive reception of a corrupt nature by means of secondary causation, e.g. the temptation of the serpent. Satan’s own reception of a corrupt nature would have had to have been on the occasion of some good, created thing. It is a sufficient defense to note that if God created Satan and other rational creatures with a capacity to be tempted and sin, there does not appear to be any reason to suppose that He could not also have created said creatures with the necessity to sin, given certain circumstances.
2. God’s knowledge of what Adam would choose was predicated on Adam’s actualizing one of two possible choices, God is not eternally omniscient, from which serious consequences for Christianity would follow.