According to kenotic christology, not only did the second person of the Trinity become a human being, but during the time that he was human, he ceased to be divine. One motivation for kenotic christology may be to avoid the difficulties of "qua" talk about Christ: "Qua human, he is only in Jerusalem, but qua God, he is omnipresent; qua human, he does not know every mathematical truth, but qua God, he is omniscient."
But this is a bad reason to adopt kenotic christology. For consider Christ's present state. Either he is still emptied of his divinity, or not. If he is still emptied of his divinity, then it is false that God is now a Trinity: God is now only a Binity. (It is, by the way, also a problem that according to kenotic christology, God was not a Trinity in 15 AD. But since God is now worshiped as Trinity but we have no record of his having been thus worshiped in 15 AD, this is not as serious a problem as God's now being a Binity.) Besides, Christ now has the "name above all other names" (Phil. 2:9), which is surely the name of God. Thus, Christ is now divine.
But Christ is also human now. The phrase "the Son of Man" is used in eschatological texts. Thus, during the eschaton, Christ will be human ("son of man" meant "human being" in ordinary Aramaic, though in eschatological contexts it had an additional layer of meaning on top of it). It would be odd, however, to posit a second incarnation. Furthermore, in the Eucharist, Christ's body is present. Surely this body is both human and alive (it would be theologically mistaken to suppose that in the Eucharist we receive Christ's dead flesh). Hence, Christ is now human and alive.
Therefore, even the kenotic christologist should admit that presently Christ is human and divine. But if the problem of the "qua" was what drove her to kenosis, she is in trouble, since it will be just as true right now as it was in 15 AD that Christ is not on Mars qua human but is on Mars qua God.
Of course, a kenotic christologist may have other motivations for positing Christ's ceasing to be divine. But the metaphysical problem of the "qua" should not be among them. For that problem is one that all Christian theologians face.
And it may be that if the "qua" problem is solved (and personally, I find a Thomistic solution quite plausible), then the other reasons for kenotic christology will also disappear.