Did Jesus say his true Church would always exist on earth in Matthew 16:18?

Matthew 16:18, Jesus says that he will build his Church and the jaws of death will never triumph over it.

Jaws of death or gates of Hell (Hell here means death - Jesus sometimes uses Hell to refer to death) could be referring to Jesus' promise of resurrection. So if believers are taken from the earth they will rise again. In that case it is not a promise that the true Christian faith will always be on the earth.
 
According to some the text says that the gates of Hell will never destroy the true Church so God will keep some Christians in enough truth to bring them to salvation so there will always be a true Church on earth. (This can be achieved without conferring infallibility – the Catholic Church uses verses like this to claim to be infallible.) The Roman Church says that the Church on earth and the Church in Heaven and Purgatory are one and the same Church. We reason then that even if the Church fails on earth that does not mean that the Lord has failed for he still has the Church elsewhere. Jesus never clearly said he meant his Church on earth would never fail. Catholics may answer that he told Peter he would build his Church on him meaning the earthly Church for the heavenly one existed then among the angels. Peter being the rock the Church was built on does not necessarily mean that he would have to be the head of the Church or that he would live up to this role. At that time, Peter was the first proper Christian. There were no saints in Heaven yet. There was no Catholic Church in Heaven or Purgatory for Jesus hadn't made saints yet. He hadn't cleaned the human race, living or dead, yet of their sin - except Peter - and formed them into the Church. Peter was the first member of the Church. So if Jesus said he was building his Church on Peter he was saying only that the Church now exists but not that it will necessarily always be on earth.
 
Jesus could still have meant that he would extend his Church to earth and build it on earth and that the Church would never be destroyed which would not necessarily mean the earth branch would be preserved forever for it is all the one Church. Some say that the true Church never fails but that men fail the true Church and let it die. This is agreeable with what Jesus said.
 
God could let the true Church on earth die for a good purpose for his ways are odd like how he waited until human beings were on the planet millions of years before establishing the true Church. This would not contradict the promise of Christ for this is not Hell overcoming the Church for it is God’s will. Perhaps he will just take it from the world because of the disobedience of believers.

The Catholic Church says that in Matthew 16 Jesus said that the gates of Hell would never prevail against his Church that Peter was the rock of. Some say that it means just the Church that Peter was the rock of that it would not be destroyed but once he would die or fail to be the rock through neglect it would have no rock and the promise would not apply then. It would be conditional on Peter's obedience. Some say Matthew 16 means that the Church that teaches the truth will never be taken from the earth and overcome by evil. Some say it means that that the Church does not fail but men fall away. In that case, the gates of Hell did not prevail against the Church but evil and stupid men did. Some say it means that enough truth would always be taught to enable some to become true Christians. This view would say that when the Roman Catholic Church taught paganism there would be some who would misunderstand it and come to the pure truth accidentally but would have been helped on the way by the Catholic doctrines that were right.
The word Church means assembly - that is all. So you can believe that there was always an assembly in the name of Christ though it was spiritually dead. Assembly only means grouping. Roman Catholicism has exaggerated it to mean family of God united in love and under one spiritual father the Pope.
 
Jesus, as the Mormon Church has pointed out, says nothing at all about the Church built on the rock as being a Church on earth. The Mormons believe that Jesus when he said that the gates of Hell would never overcome his Church meant that even if the Church ceased to exist on earth it would exist in Heaven. Catholics assume that Jesus meant the Church would always exist on earth and be built on the rock of Peter and the papacy. Mormons say that Jesus spoke of the gates of Hell fighting his Church which means he was thinking primarily of the Church in the spirit world for Hell was part of the Spirit world. They say that Satan need not necessarily approve of every human effort to destroy the Church. They say there is no need to believe he is behind all such activity. They say Jesus mentioned only Hell fighting the Church and not people which implies he was not primarily thinking of the Church on earth. If so, then Peter was not the earthly rock that the Church was built on. Jesus talks about giving Peter the keys of the kingdom of Heaven - again seemingly thinking of the spirit world. The idea of Peter being pope in the spirit world is ridiculous. The Mormons to their credit came up with a very good interpretation of Jesus teaching about the Church being immune from the powers of Hades.
 
Many considering the Roman Catholic claim to be the true Church of Christ that hell would never get the better of, would say that since the vast majority of Christians are outside the Catholic Church that the Roman Church cannot be this Church at all. The real Roman Catholic Church is actually tiny. The Catholic Church holds that all who are baptised belong to the Catholic Church despite their membership of different denominations. So they were made Catholics but didn’t know it. It follows then that the Catholic Church is full of splits and schisms. That does seem to be a great triumph for hell. It gets worse when you realise that people professing to be Catholics doesn’t actually make them Catholics.  The Church holds that any Catholic who knows what the Church teaches and refuses to accept it is ceasing to be a Catholic. Canon Law decrees automatic excommunication for such.  The vast majority of Catholics these days have no regard for Church teaching authority. Polls depress the Church showing how many refuse to believe that the bread and wine of the Eucharist become the body and blood of Jesus Christ and scoff at other Catholic doctrines such as papal infallibility or the divinity of Jesus Christ. So it follows that only a small number of people can properly be called Roman Catholic. If the small number isn’t a triumph for hell then what is? If there is no true Church on the earth at all that isn’t very different from there being a tiny true Church,
 
If you believe that sincere people are members of the Church of Christ without knowing it you could still hold that all the professing Christian Churches are apostate. If Jesus meant a spiritual Church or invisible Church and that this was the Church over which hell would never triumph as virtually all Protestant theologians contend then the verse doesn’t refute universal apostasy.
 
Matthew 16 is the only place in the Bible that really seems to predict that complete apostasy from the faith will never happen. It doesn’t so the idea that Christians would leave the faith as a whole is compatible with the Bible.