Perhaps the most telling failure in Thomas’ presentation of divine immutability is the inability of this immutable God to do anything new. Because God is actus purus, there is no conceivable sense in which God can do a new thing. In other words, what’s done is done. God is static and immovable, and no new event can ever occur. This of course is hard to square with the biblical narrative; one has to assume that the experience of newness in relation to God is simply a phenomenological illusion.
But in fact, Aquinas does hold that there is a conceivable sense in which God can do a new thing; because potency or potential can be understood to refer either to active power or potential power, and the latter is the only one that conflicts with immutability. Immutable is not static -- although it's easy enough to see why one might think so, given what the term has come to mean. Immutability is a characteristic distinguishing Creator from creature: things that are mutable are dependent on an extrinsic power. The point of saying that God is immutable is to say that God is not so dependent. This can be seen in a different way (cf. ST 1.9.2). Creatures have a potential for being changed by something else either with regard to their substance and everything depending on them (as in the case of things that naturally go in and out of existence), or with regard to place only (we know of no such things, but Aquinas like most medievals assumed that celestial bodies are such), or with regard to the different ends they can assume and objects their capabilities can take (as with angels); since all these things can be affected by God, who governs their existence and non-existence, all these creatures are mutable with respect to the divine power. But God is subject to no other power in any of these ways: He doesn't go in and out of existence; He doesn't move from place to place; and no one can determine His ends and objects for Him. And since that's exhaustive, God is immutable. But this is an affirmation not of any inability but of a power that has no weakness. Somewhere, I forget where at the moment, Aquinas says that immutability is the strength of God.* And this pretty much sums up Aquinas's view: to say that God is immutable is to say that nothing else is stronger or more powerful than He is in any way; He can do as He wills, and nothing else has the force to turn Him or change Him or make Him undergo anything; neither His essence nor His action admit of any weakness.
* It seems to be Gilby's translation of ST 1-2.61.5. It's a bit loose, since what Thomas strictly says is that God's fortitude is His immutability. But it's not far off, either, since the point is that what we call fortitude is expressed with complete perfection in divine immutability. So if you want to understand what Thomas has in mind when he talks about immutability, a good way to do it is to start with the virtue of fortitude and to think of what's involved in a fortitude that can never fail. In Thomas's view (ST 1.50.5 ad 1) immutability goes with fullness of life and immortality, while mutability is a sort of subjection to death.