1. Why did Jesus' prophecies about His soon return fail? Doesn't that prove Jesus is a false prophet? Secular critics press this issue.
2. If Jesus is the Messiah, how come the Kingdom of God with all its promised blessings including the defeat and elimination of evil, the arrival of world peace and universal prosperity not come to pass? This is especially pressed by non-Messianic Jews. Since they see those things as the indications of the arrival of Mashiach/Messiah.
I think Partial Preterism does a great job at responding to the first objection. The problem is that some partial preterists eventually come to full preterist conclusions. And among those, some take it further and conclude that Jesus was a failed prophet because the resurrection of the dead didn't take place [among other predictions]. So, the preterist response has its minor drawbacks and disadvantages.
I also think Postmillennialism can do a lot to lift some of the burden and release some of the pressure of the second objection. As Isa. 9:6-7 says:
7 OF THE INCREASE OF HIS GOVERNMENT and of peace there will be no end, on the throne of David and over his kingdom, to establish it and to uphold it with justice and with righteousness from this time forth and forevermore. The zeal of the LORD of hosts will do this.
Jesus' parable of the leaven leavening the whole lump takes time [Matt. 13:33]. So does the increase of Messiah Jesus' government. The stone of Dan. 2:35 gradually grows to fill the whole earth. It doesn't arrive from heaven and land on earth fully grown as a mountain [representing the Kingdom of God]. It arrives as a stone that grows like a seed.
Matt. 13:31 He put another parable before them, saying, "The kingdom of heaven is like a grain of mustard seed that a man took and sowed in his field.
32 It is the smallest of all seeds, but when it has grown it is larger than all the garden plants and becomes a tree, so that the birds of the air come and make nests in its branches."
This parable of the mustard seed is a clear allusion to Belteshazzar's vision of a great tree that represented his kingdom that was to be judged [Dan. 4]. Whereas Belteshazzar's tree/kingdom was chopped down, Jesus' mustard tree grows and remains.
Jason cites Ps. 110:1. There's a sense in which 1 Cor. 15:24-26 is the apostle Paul's exegesis and application of Ps. 110:1, and it has postmillennial implications. See the following article:
AN EXEGETICAL DEFENSE OF POSTMILLENNIALISM FROM I CORINTHIANS 15:24-26: The Eschatology of the DIXIT DOMINUS by Gregg Strawbridge
Critics of postmillennialism often object by pointing to present world problems as undermining the viability of the postmil position. But that's looking at history in our short lifespan. When the big picture of history is viewed, it's clear that the world has gotten better since the coming of Christ. A lot of it has to do with the influence of Christians and the Christian worldview and it's affects on science, human dignity, morality, philosophy, government, economics etc.
There were multiple comings of Yahweh in judgment on various nations in the Old Testament using the same cosmic language used by Jesus. Given that background it's highly likely that some form of preterism is true [partial preterism is within the bounds of orthodoxy, but full preterism isn't]. In which case, Jesus' coming did happen in 70 AD with the destruction of Jerusalem just as He predicted. That leaves room for a final coming of Jesus to usher in the New Heavens and New Earth/Eternal State. See Kenneth Gentry's books and mp3s on the subject. Also Gary DeMar's books.
For a good introduction to partial preterism either watch R.C. Sproul's freely available lecture series "The Last Days According to Jesus" linked below, or read his book with the same title.
Hampden-Cook's book argues for full preterism, and Russell's nearly does so. But I recommend them nevertheless because much of what they contain can be used to support partial preterism and weaken the objection that Jesus was a failed prophet.
Refuting the errors and heresy of Full Preterism:
Read Ken Gentry's and Sam Frost's critiques of full preterism. Frost himself was once a full preterist.
Why I Left Full Preterism by Sam Frost;
When Shall These Things Be?: A Reformed Response to Hyper-Preterism by Keith Mathison and other authors;
Have We Missed the Second Coming?: A Critique of the Hyper-preterist Error by Kenneth Gentry
Neither partial preterism or postmillennialism need to be true to weaken the force of the two original objections. Even if false, opponents of Christianity have to refute preterism and/or postmillennialism if they are going to continue using those objections.
The added advantage of appealing to both preterism and postmillennialism is that there are multiple lines of evidence for their truth, and those evidences support the inspiration of the Bible because it involves the 1. fulfillment of Jesus' predictions of judgment, and 2. the fulfillment of the prophecies in both the OT and NT of the Messiah's reign spreading around the world.
Christianity is the world's largest religion, and as a living philosophy and way of life it has had more impact on the world [past and present] than any other ideology/worldview. Maybe Moses has had more influence than Jesus. But if Christianity is true, then that falls in line with and adds to Jesus' influence. Since Moses is a forerunner and Biblical type of Jesus. Some might say that earlier ideologies and religions may have also influenced Judaism and Christian. In which case, they they have had more influence. For example, Zoroastrianism et alii. But those are not living, but virtually dead philosophies of life. Besides, if Christianity is true, then given Common Grace we'd expect the positive aspects of non-Christian ideologies to have some influence on or have parallels to Christianity. Whether Persian religions, Greek philosophy, Roman law et cetera.