Answer
The simple answer is: yes and no. We can speak of God dying only if we mean that Jesus, the person who was God, died. The problem is that we cannot say that Jesus died in his divine nature. He only died in his human nature. (This is not the same thing as saying that his human nature died; natures don't die, persons do.) It would be just as impossible for Jesus to have died in his divine nature as it would be for the Father or the Holy Spirit to die.
One way to argue this is to say that life is an aspect of God's character, and that his character is immutable. For God to die would require a mutable character, therefore God cannot die.
In any case, it was only necessary that Jesus die in his human nature. The fact that Jesus had a divine nature ensured that his human nature would be and would remain perfect, but it did not enable him to offer the atonement. What made him able to offer the atonement was his perfect human nature. He had to be human for two reasons:
First, he had to be heir to the covenants between God and man (i.e. Adamic, Noahic, Abrahamic, Mosaic, Davidic). In his divinity Jesus was not heir to the vassal side of these treaties/covenants.
Second, he had to be made flesh and blood like those he was redeeming in order to make propitiation for their sins (Heb. 2:14-17). Since we are not divine, he did not need to be divine to propitiate for us.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.