A good (audio) overview of local church autonomy is found here.

Specifically, as an answer to the Jerusalem Council, James White argues that it was a meeting between two specific churches, and it was apostolic as well. So, since that office is no longer in existence, such a Council would not be repeatable. The Council also claimed divine inspiration in Acts 15:28-29.

In the bigger picture, you don't see any sort of presbytery structure in the New Testament. Why didn't Paul lay down qualifications for those in any offices higher than elders? Why did Paul write to the church at Corinth instead of writing to the Presbytery of Asia Minor? Why were the warnings against false teachers given to local churches and not also to presbyteries?

True godliness is a sincere feeling which loves God as Father as much as it fears and reverences Him as Lord, embraces His righteousness, and dreads offending Him worse than death~ Calvin