I'm wondering on this one. I'm reading Eusebius and he states that at least one letter from the Bishop Clement (c. 35 AD - 99 AD) to Corinth was considered worthy to be read and was circulated among the early Church in the first and second centuries. Why was it not included in the canon?
I don't believe that we can discern exactly why the Church Fathers considered certain writings as belonging within the New Testament canon and others not, but those writings that were included in the canon - with the notable exception of Paul's Epistles - were either written by those who were direct disciples (though not necessarily Apostles) of Christ or were documenting what His direct disciples had witnessed. Examples of the latter might include Mark, who early Church histories maintain received his Gospel from Peter; and Luke, who was not an Apostle, but - as at least held in the eastern Church - was one of the Seventy and was Cleopas' companion on the road to Emmaus (Luke 24).
It should be noted that prior to the New Testament canon being formally closed for the entire Church at the 7th Ecumenical Council (787), Clement's Epistle did appear in some New Testament manuscripts - most notably the Codex Alexandrinus, dating to the early 5th century.