Did the Holy Spirit abandon Jesus on the cross?
Around the ninth hour, Jesus shouted in a loud voice, saying “Eli Eli lama sabachthani?” which is, “My God, my God, why have you forsaken me?”
Matthew 27:46
No one who contemplates this cry from Jesus can help but get a chill up their spine. The quote is also in Mark and this adds to the reliability that it is authentic. In addition, it is somewhat troublesome, and so it's unlikely that it was added later by some well-meaning monk (as is the case with some other quotes in the Gospels).
So, what does it mean? Consider this possibility: Upon his baptism by John, Jesus has a mystical experience, connecting directly to God. He manages to maintain that mystical union with God for three years until the suffering from the crucifixion is just too much for him. He can't hold the connection, and cries out as he loses it.
If you re-read all of the New Testament passages about the Holy Spirit, you will note that in each one of these references something is happening (descending, swirling, etc.). If you remove your “First Council of Constantinople” blinders, you will see that the Holy Spirit is the Spirit of God in people and not a thing-in-itself. Early Christians, mostly not as used to abstract thought as, say, Greek philosophers, would have had a hard time “getting” this concept. Thus, like so many other examples of reification in the history of religion, what was an abstract idea became (literally) personified. God-in-humanity became the third person of the Trinity.
It turns out that maintaining your connection to God is hard, even if you're Jesus.