Christian materialism holds that the human being is a fully material entity, with no immaterial soul. Here is a problem for this view: What happened, on this view, when Christ died? After all, death is the destruction of the body.
Option 1: He ceased to exist. This option is distinctly unsatisfactory theologically—Christians have never believed that. On the contrary, Christians believed he descended into sheol to draw out the souls of those awaiting him there. And if God is omnitemporally eternal, it has the consequence that one of the persons of the Trinity ceased to exist, which is contrary to divine eternity.
Option 2: He ceased to exist qua human. But this simply means that the Incarnation ceased for the second person of the Trinity, and he was back to the state he was before the Incarnation. Since the Incarnation was not a gain for him, neither was this any loss. But then the sacrificial meaning of his death is undercut.
Option 3: He continued to exist, because a chunk, or the whole, of his brain was miraculously preserved, and then that brain piece or that brain descended into sheol to draw out the souls awaiting him. This seems implausible. Moreover, unless something like this happens for all of us (Peter van Inwagen played with this option), then his death was radically different from our deaths, which is theologically problematic. And if this is what happens to all of us, then death is not as evil as it seems—it's really just like an amputation of a lot of one's body, but not of all of it.
Option 4: He continued to exist, and so the Logos was the dead body of Christ. This view is similar to the orthodox view that the dead body of Christ was still united to the divinity. But do we really want to take the further step of saying that the Logos was a dead body?