I have been pondering this question for several weeks now, but I think I have found an (uneasy) resolution. Here's the crux of my question. Matthew 24:36 // Mark 13:32 speak of the Son not knowing the hour (of the second coming). What does the second person of the Trinity know, after he has taken a human nature to himself?
Francis X. Gumerlock provides Four Patristic Solutions to the problem. Here they are briefly summarised:
1. Basil of Caesarea argues that the verse in Mark should be read as "not the Son, if not the Father", thus a statement of Christ's unity with the Father and the basis for his knowing the time of his return.
2. Augustine argues from scriptural parallels that 'to know' can mean 'to reveal', and that this is the sense here. The Son does not reveal the hour.
3. Gregory of Tours argues that 'son' is metaphorical for the church (sons of God), and 'father' is metaphorical for Jesus.
4. Athanasius (and following him Gregory Nazianzus (who prompted this whole conundrum for me), and Rufinus) follow an anthropological solution. He knows as God, He knows not as Man.
Of these 4, Basil's runs aground on the Matthean passage. Augustine's position works from good scriptural warrant on the meaning of 'to know', but overstretches its meaning here. Gregory of Tours is, I believe, the weakest. Athanasius' is the strongest, but the danger is a veering towards Nestorianism.
The problem comes post-Chalcedon. In response to Nestorianism, it was held that the Son knew and was not deficient in knowledge in this regard, due to the unity of the two natures. This is, it seems, a reaction to the position that somehow the Divine Nature within Christ sometimes informed, sometimes withheld knowledge. It seems, however, an overreaction to say that the Human Nature was "fully enriched with the fullness of divine knowledge" (Gumerlock, supra.)
I pass now to Calvin, in his Commentaries on the Synoptics, particularly on this verse. Calvin argues that each nature retained its own properties (contra the Lutheran version of the communicatio idiomatum), and that at times the Divine nature 'reposed' within the incarnate Person, that the Son might act in his human nature, according to his mediatorial work.
The strength of Calvin's position is that he is sharp to articulate the two natures without confusion, and without suggesting that the Divine nature is circumscribed by the limitations of the Human. He is also right to refer this statement to the dispensation and mediatorial mission of the Son at that time.
Lastly, I consulted Grudem's Systematic Theology, which may seem a rather odd place to end up. Grudem does treat of this question in his exploration of Christology, and his answer I found immensely helpful.
Grudem reminds us that not only do we confess two wills in Christ, Human and Divine, but also two intellects. If that is so, then we may well say that the Son knew things in his Divine nature, which he did not know in his Human. I confess, I find it incredibly difficult to predicate of the same subject, the Person of the Son, both knowledge and ignorance in respect to the same object but with respect to distinct Natures. Nonetheless, I think Grudem has the right of it, in extending the line of thought of Athanasius, Gregory of Nazianzus, and Calvin.
So, I think I am resting my case.