Some people have suggested that Acts 1:29-31 means that the Church will vanish in apostasy -- but all it says is that false teachers will be found in the Church. It does not say that they will occupy all these positions, or even the majority.
In 2 Thessalonians 2 we have a stronger warning. A time of rebellion is named where a man claims to be God and deceives many -- but it is clear that if you read on through the chapter that the believers are not affected by the delusion and the essence of the Gospel is to be always preserved.
Remember Matthew 13:24-30 in which Christ tells us that the Church will contain both wheat and weeds. If the Church ever perished, there would be only weeds and nothing to stay the hand of judgement and destruction, no reason for the Lord of the Harvest to refrain from pulling up the weeds -- for the parable tells us that he does not pull up the weeds to spare the wheat (the believers, the saved).
Thus, I suggest, that we may all take comfort in God's defense of the Church. We can look to it and be assured that in every age of human existance since Christ's crucifixion, the Church has remained -- sometimes suffering, sometimes persecuted, sometimes losing members, sometimes gaining, but never perishing, but always a pillar and bullwark of truth (1 Tim 3:15).
This also means, however, that we should look at the entire history of the Church and the doctrines of Christ as Christians have believed them to help us in our present interpretations of Scripture. Of course, some ages may be more useful to consult than others.