Apostolic presence is critical because the original apostles (I'm speaking here of the eleven plus Paul) spent much time directly with Jesus Christ. If anyone was in a position to know what Christ's expectations are for his church, these are the men. Additionally, the apostles were given at least some unique authority in decision making as it relates to the church.
We learn in Ephesians that the apostles are part of the foundation of the church:
Ephesians 2:19-20, "So then you are no longer strangers and aliens, but you are fellow citizens with the saints and members of the household of God, built on the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone."
We see numerous examples of apostolic authority in passages such as the following:
I Corinthians 4:19-21, "But I will come to you soon, if the Lord wills, and I will find out not the talk of these arrogant people but their power. For the kingdom of God does not consist in talk but in power. What do you wish? Shall I come to you with a rod, or with love in a spirit of gentleness?"
I Corinthians 11:17-22, "But in the following instructions I do not commend you, because when you come together it is not for the better but for the worse. For, in the first place, when you come together as a church, I hear that there are divisions among you. And I believe it in part, for there must be factions among you in order that those who are genuine among you may be recognized. When you come together, it is not the Lord's supper that you eat. For in eating, each one goes ahead with his own meal. One goes hungry, another gets drunk. What! Do you not have houses to eat and drink in? Or do you despise the church of God and humiliate those who have nothing? What shall I say to you? Shall I commend you in this? No, I will not."
I Corinthians 14:37, "If anyone thinks that he is a prophet, or spiritual, he should acknowledge that the things I am writing to you are a command of the Lord."
Paul gives repeated reminders that his position as an apostle comes not from man but from God. For example:
Galatians 1:1, "Paul, an apostle - not from men nor through man, but through Jesus Christ and God the Father, who raised him from the dead."
Within the evangelical church we tend to downplay the importance and authority of the apostles. My guess is that we do this as a reaction to Roman Catholic abuses related to prayer to the apostles and other such nonsense. We must be careful, however, to form our understanding of apostolic importance based on scripture and not simply because of a reaction to what others believe.
The reality is that Jesus Christ did give his apostles unique authority within the church. They were by no means dictators. First and foremost, they were to serve the church in a manner that glorified Christ. We know that they did a great deal of teaching. This makes sense since they, as stated above, spent so much time with Jesus.
The apostles taught a great deal about the church. In the book of Acts, we see them involved from the very beginnings of the church. This extends all the way to Rome, with Paul under house arrest but preaching the gospel unhindered.
We know that when problems arose in the church the apostles stepped in and addressed them. This sometimes took place with the apostles present, such as the case of Ananias and Sapphira in Acts 5. Many other times the apostles, especially Paul, corrected church problems from a distance through epistles. Just reading I Corinthians shows us this.
The apostles did not tell each church how to function to the smallest detail. However, they did give many instructions that, led by the Holy Spirit, were designed to shape the church in a manner that would honor Christ. Their presence ensures that the practices of the early churches were either acceptable or corrected. We know enough of the apostles to realize that when practices were unacceptable, they wrote or visited to bring them in line with God's expectations.
What does this mean for us today? As we think about church life, we must remember that the apostles were present in the early church. The apostles made great efforts for the church to be what Jesus wanted it to be. They taught and rebuked under Christ's authority. They corrected what needed correcting, and gave approval where the church functioned as it should.
In light of this, when we are dealing with church issues, we should always look to see what the apostles taught about certain issues. We ought to also look at how the early church functioned as a group and as individuals. We don't need new ways of doing things. We don't need to figure things out on our own. The scriptures themselves show us the church as the apostles thought it should be. They should have known. After all, they were with Jesus, the Head of the church.