I have Protestant family members that argue the Gap Theory against Apolostolic Succession. They argue (Based on books they have read by other Protestants) that:
Succession lists of Catholic Bishops (and of the early Popes) have gaps in them and therefore Apostolic Succession is not completely unbroken. I’m not sure where they are getting this particular allegation.
The Early Church (Particularly in the East) were under a Body of Men (Presbyteros) as in the New Testament. They argue that in N.T speaks of Presbyteros (Plural) appoint in every town. This in their mind refutes any notion of a local Church under one Priest. In their mind, the present day Non-denominational Fundamentalist churchs more closely resemble the New Testament Church in form governance.
Any authority given to the Apostles like the power to forgive sins (Jn 20:22) ended with the Death of the Last Apostle.
I’m looking for some good answers. Finally, I might note that because of their argument (of #3) they feel free to dismiss any of the teachings of the Early Church Fathers especially with regard to the Real Presence of Christ in Eucharist. In practice Fundamentalists I know will give more credience to Today’s Bible preachers (J. Vernon McGee, Jimmy Swaggar, Billy Graham, etc) than someone like Polycarp who knew St. John personally.