My feeling, coming from the literary side of the house (which is to say my study of mythology and language is for the purpose of creative endeavor,) is that Frazer's ideas never went away--it was merely the scholarship that was disputed. Serious scholarship is distinct from "poetic truth".
I see Frazer's influence in writers like Eliot, Yeats and Robert Graves, who themselves had a significant impact on 20th century literature.
I saw a staring virgin stand
Where holy Dionysus died,
And tear the heart out of his side.
And lay the heart upon her hand
And bear that beating heart away;
And then did all the Muses sing
Of Magnus Annus at the spring,
As though God's death were but a play.
Source: Two Songs from a Play
The play referenced in the title of the poem is Yeats' The Resurrection. Theologians and scholars can analyze the subject ad infinitum, but from the standpoint of mythology and literature, these views will always be secondary to the work of the great poets, and Yeats is certainly one of those poets who can stand alongside the greatest poets of antiquity. In other words, Yeats contributes to, and expands, the canon. His literary capability and insight, in conjunction with his status, make him eminently qualified to do so.
More lately this influence is strongly seen in creators of mythology such as Neil Gaiman and Alan Moore, who had a similar impact on their mediums as Eliot and Yeats had on poetry. Lovecraft, another author influence by Frazer, produced work that has been widely mythologized in subsequent work. In essence, Lovecraft creates a new mythological canon. These are just a few examples.
It is just as compelling and as relevant today as when Frazer wrote about it.
In a religious context, one way to regard this archetype is as the mythological component, distinct from the ethical component. From this perspective, Jesus' main function as Messiah was the introduction of the new Golden Rule: the love of the other as the self.
(This idea was presented by Hillel, and subsequently reinforced by Akiva in the Common Era, with the idea that "the rest is [merely] commentary". In those cases, they were referring to the Old Testament, but the same case can, and has, been made for Christianity.)
Post-Nash the Golden Rule has has found mathematical validation in the superrational strategy, liberating the ethical component from the mythological.
Yet I still think the decline/generation model is extremely relevant--Game Theory may be cast as the mathematical analysis of equilibria and cyclic models are quite important. Economies, cultures and civilizations, not just nature, run on cycles.