Why didn't the Archangel Michael save Jesus when he was crucified?

There are some things about Jesus divinity which need be understood in consideration of your question. We must first understand that when we subscribe to the concept of the Trinity; we are accepting that Jesus is a third part of God. The other two parts of God being the Father and the Holy Ghost. Angels are not creatures with free will as are Mankind. Angels are only capable of doing the will of God; since they are incapable of weighing the options. Jesus as a third part of God therefore has the power to direct the actions of Angels; and as shown by DJClayworth Jesus did not want any interference with his execution of the will of the Father.

John 5:30 KJV  I can of mine own self do nothing: as I hear, I judge: and my judgment is just; because I seek not mine own will, but the will of the Father which hath sent me. 

Jesus came into this World for only one purpose; and that was to reclaim the lost to the Father. Since Jesus purpose for coming to earth, in the first place, was to bring back God's creation to him, anything less would have been to waste his coming.

John 6:39 and 40 KJV  And this is the Father's will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day. And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day.

Here Jesus is making reference to the Great White throne judgment.

 Revelation 7:9 through 15 KJV  After this I beheld, and, lo, a great multitude, which no man could number, of all nations, and kindreds, and people, and tongues, stood before the throne, and before the Lamb, clothed with white robes, and palms in their hands; And cried with a loud voice, saying, Salvation to our God which sitteth upon the throne, and unto the Lamb. And all the angels stood round about the throne, and about the elders and the four beasts, and fell before the throne on their faces, and worshipped God, Saying, Amen: Blessing, and glory, and wisdom, and thanksgiving, and honour, and power, and might, be unto our God for ever and ever. Amen. And one of the elders answered, saying unto me, What are these which are arrayed in white robes? and whence came they? And I said unto him, Sir, thou knowest. And he said to me, These are they which came out of great tribulation, and have washed their robes, and made them white in the blood of the Lamb. Therefore are they before the throne of God, and serve him day and night in his temple: and he that sitteth on the throne shall dwell among them.

This is the reasoning behind Salvation, Who those are; who Jesus referred to as those which the Father has given me. or as John described in John Chapter 0ne.

 John 1:1 through 5 In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God.  All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men.  And the light shineth in darkness; and the darkness comprehended it not.

From verse 3 we learn that Jesus Created all things. This explains what Jesus meant by his statement:

John 6:39 and 40  And this is the Father's will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day. And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day.

And those who the other two parts of the Trinity have given him are:

John 3:16 through 18 KJV  For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. For God sent not his Son into the world to condemn the world; but that the world through him might be saved.  He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.

So what we learn from this is that God in his anger; would destroy all creation, but has acquiesced to give Jesus those for whom he assumed their sins and suffered the penalty given to Adam as punishment for disobedience. We can almost hear God telling Michael and the other Angels to destroy all creation, and then at the intervention of Jesus, allowing Jesus to redeem a part of his creation, and having the Angels put off their destruction until the end times.

Revelation 21:1 through 4 KJV  And I saw a new heaven and a new earth: for the first heaven and the first earth were passed away; and there was no more sea. And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband. And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God. And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away.

We are left to assume that God in his anger has decreed that all creation is to come to utter destruction, but has graciously allowed Jesus to reclaim a small portion of his creation; to move to a new creation where God will create a perfect atmosphere to go into Eternity. And the reason for the Angels not saving Jesus at the cross was their having been on a temporary hold by God in order for Jesus to reclaim those believers in not only Jesus divinity, but also his passion for having those which he created in the likeness of God. That likeness is also a trinity including body, Spirit and Soul.