We need to consider the context in which this verse is found. Here is my translation of Philippians 2:10-11 (because it is a sensitive passage, I want to give a defensible and, as far as possible, neutral translation):1
If there be any consolation in Christ, if there be any comfort of love, if any community of spirit, if any tender care and compassion, 2 fulfill you my joy: that you be of the same mind, having the same love, united in soul, being of one disposition—3 not of strife, nor vainglory, but in humility deeming one another greater than your own selves, 4 each one not regarding the things of himself, but the things of others.
5 Let this disposition be in you which was also in Christ Jesus: 6 who, being by nature in the form of God, did not deem equality with God robbery, 7 but emptied himself, taking the form of a slave, being made in the likeness of men. And being found as man, 8 he humbled himself to the point of death: even the death of the cross. 9 For which reason also God greatly exalted him, and gave him the name that is above every name: 10 so that at the name of Jesus every knee should bow—of those in heaven, those on earth, and those under the earth—11 and every tongue confess that Jesus is Lord, to the glory of God the Father.
St. Paul invokes Christ as an example of "this mind" which the Philippians, and by extension all congregations, are to emulate. How is He depicted as having such? St. Paul writes that He regarded "not the things of himself" but those of us (namely, our salvation on the Cross). Where does He described the things Christ gave up for us? He describes them when He says, "being by nature in the form of God," whence He has "equality with God" (Cf. John 10:33), and then that He took instead "the form of a slave." He had both in truth—He really became a servant, and He really was God. Equality with God was "his own" (v. 4). And having the former was not illegitimate, which is why it is described as "not" the result of pillaging or robbery, or something ill-gotten. In fact, he uses two synonymous words for "take." The one, translated here "robbery," and the other, "taking," are correlatives—one describes the taking of something by force, such as a robbery or pillaging, and the other is a free receiving or taking (hence the reflexive, "emptied himself," and then the "taking"). He does this to show that equality with God is Jesus' right, and is natural ("by nature" or "naturally being") to Him, but that He freely took (ελαβεν) "the form of a slave" (which contextually means a human nature: Cf. John 1:14; Romans 1:3-4; Galatians 4:4)—the very greatest example of humility possible, hence St. Paul's choice of Christ's incarnation.
There may also be a play on words, or interplay between words, in the Greek because St. Paul excludes "vainglory" (κενοδοξιαν) from the Christian mindset, and praises the "emptying" of Christ (εκενωσεν) who really has a glory worthy of praise instead. Both use "empty" (κενος), except one is a praiseworthy self abasement inspired by humility, and the other is essentially glorying in emptiness: Jesus empties Himself as it were of His heavenly glory, whereupon God bestows upon Him that glory again, a kind of divine refusal to allow any prolonged humility to the deserving of glory (Cf. Matthew 23:12).
So since He is said to be naturally God, not naturally man, but that He is God and became man at a point in time, clearly He cannot cease to be God—"the First and the Last" (Revelation 1:17) cannot by definition be 'an Early One and One of the Later Ones;' the "I am" (John 8:58) cannot be simply the 'I was.'
The debasement or emptying is the taking on of the human nature and suffering in it, not necessarily in the giving up of the divine!
1 Translated from the Nestle-Aland Novum Testamentum Graece 28th Edition.