That's why I find the same deep comfort in God's non-death that the psalmist did.
"My days are like an evening shadow; I wither away like grass," he writes in Psalm 102. "But you, O Lord, are enthroned forever; you are remembered throughout all generations. ... They will perish, but you will remain; they will all wear out like a garment. You will change them like a robe, and they will pass away."
This psalmist has no name, he is simply called "one afflicted, when he is faint and pours out his complaint before the Lord." Death is troubling. It is painful, heart-breakingly so. That's why there is intense comfort in God's eternality, the fact that He has no beginning and no end, no birth and no death.
The Bible calls death a curse. Even though God redeems our suffering and uses it for His purposes, death is still a result of the Fall, of the curse that came with sin. That's why God's non-death is such good news.
When I was little, I hated to be the only one awake at night. I felt alone if everyone else was asleep - especially Dad since he was always up the latest. So a way that I comforted myself was with the thought that God never went to sleep. That feeling of strength and protection that I had when Daddy was awake I focused on God. God was always awake, He was always protecting me, and I felt safe and comforted.
In a way, that is how God's non-death ministers to us. When those we love pass away and we begin to feel alone, we have a Rock who never dies. Death is a bitter and lonely companion, but what a friend we have in Jesus. Even in our darkest times, we have a Father who never falls asleep. This is the intense comfort of our God's non-death.