Louw-Nida agrees that there are "contexts in which YUXH refers to existence beyond death" (26.4), though in such contexts "it may be referring figuratively to the person" (citing Acts 2:27 as an example). Their identification of APOLLUMI THN YUXHN as an idiom meaning "to experience the loss of life, to die" (23.114) does not prejudge the question of what happens at death. (It does, though, support my claim that APOLLUMI in this context means something more like "cause to be lost" than something like "render nonexistent.")
πορεύεσθε δὲ μᾶλλον πρὸς τὰ πρόβατα τὰ ἀπολωλότα οἴκου Ἰσραήλ (Mt 10:6 WH).
"Go instead to the lost sheep of the house of Israel" (NET Bible).
The translation "lost" works in Mt 10:6 since the context and other parts of the NT indicate that Jesus' disciples are hunting for those who are spiritually "lost" rather than spiritually "destroyed." Yet the gathering of sheep is not under consideration in 10:28: the verse specifically mentions Gehenna along with the destruction of soul and body. Furthermore, Luke uses τὸ ἀποκτεῖναι and ἐμβαλεῖν εἰς τὴν γέενναν in the parallel account thereby indicating that the "loss" of body and soul is not the issue (Luke 12:5); the writer is concerned with divine "killing" and the possible annihilation of unfaithful ones. Being thrown into Gehenna figuratively depicts this everlasting destruction of body and soul, and not simply the death of the former or the latter.
In Mt 10:39 and 16:25-26, the rendering "lost" is appropriate in view of the contrasts set up by Matthew between "find" and "lose" or "win" and "lose." Mt 10:28 does not have this type of chiastic contrast.