I've been reading Paul Hinlicky's new book Divine Complexity. The premise of the book is actually wrong (he doesn't get the classical idea of divine simplicity, but that's for another post), but there's still quite a lot of good things in it.
One good point that he makes is that the Cappadocian Fathers and other early theologians who asserted divine immutability didn't think about it quite in the same way as Plato or Platonizing Christian and Jewish theologians did (i.e. Philo, Origen, Clement, Justin Martyr, etc.). For the Cappadocians, God is conceived as something living. Even though he is immutable, his immutability is not something static. God is unchanging "energy."
I was thinking about this, and I think the best analogy of the Christian concept of immutability and that of Plato is ice vs. fire. For Plato, God or "the Good" is like ice in his immutability. It's frozen. If it moves, it breaks- in other words, it loses its integrity. I think that's essentially why Arius taught what he taught. If God could act and enter our story, he would break. So, Jesus isn't God. He's a go-between so that God can stay God and not break.
By contrast, the classical Christian idea of immutability is that of fire. Fire is living, yet it doesn't change. It stays exactly the same if you keep on putting fuel on top of it. It can also spread, while not losing anything of itself or changing. This is because the Biblical doctrine of immutability is rooted in the Trinitarian conception of God. The Trinity is dynamic. It is an eternal event of divine self-communication and donation. It doesn't change, yet it is living and dynamic. The Father gives all of himself to the Son, while remaining the unchanging Father. God exists as a relational life. He isn't a slab of ice, but a living, yet unchanging, reality.
I think this is a better model of Christians to understand the immutability of the divine being. Understand God as something living, yet unchanging also helps us starve off the attacks of those who (based on a false understanding of immutability) what the divine being to be mutable. If that latter would be true, it would destroy the whole Christian account of God. It would mean that creation would be deified and present possibilities to God which he lacked in himself. Even worse, God might be change his mind about either the law or the gospel. The end result would be that the divine assurance that the gospel brings would be utterly destroyed.