Dr. Vallicella, in his reply to a criticism of his criticism of a reduplicative argument about the nature of the Trinity, writes:
It is a necessary truth, indeed an analytically necessary truth, that anything divine is immortal.
This claim might pass muster among some philosophers, but it would be roundly booed by folks in the field of religious studies*. If "immortal" means "not subject to death," then I'd argue that many traditions claim their divinities to be mortal. Buddhism views all gods (and asuras, apsaras, hungry ghosts, etc.) as subject to the laws of karma and therefore mortal. The Norse tradition (thanks for the reminder, Mike) claims this as well. With enough digging, I could find other pantheons in which gods die and/or disappear.
In fact, it could be argued that Christians attribute mortality to God-- it's one of the paradoxes of the Incarnation and, historically, one of the sources of Christian antisemitism (see, for example, accusations of "deicide").
I'd find it hard to make the claim that immortality is an analytically necessary attribute of divinity, when the historical record of thought on the matter indicates otherwise. What does Vallicella mean by "divine," and does his definition match that of the great traditions? Specifically, does it match whatever received Christian definitions are out there? If it does not, then Vallicella's claim about the nature of divinity night represent a straw man, possibly affecting his larger exploration of the coherence of trinitarian doctrine.
UPDATE: To be clear, my only concern in this post is with the definitional issue: what does "divine" mean? What does "immortal" mean? And why, given the actual claims about divinity made throughout history by the different traditions, does Vallicella part with those traditions to say that immortality is an analytically necessary attribute of divinity?
*An admittedly vague term. People in this field, and I'm one of them, are still defining what the term means.