Why were none of the Apostolic fathers' writings included in the last canon accepted in the Ecumenical Councils? Why is it so that none of the Apostolic fathers' writings was included in the last canon accepted during the time of the Seven Ecumenical Councils?

By the "last canon" I mean the one that we have until today.

From the wikipedia article on the Development of the New Testament Canon I learned that Irenaeus of Lyons considered the letter to the Corinthians, known now as 1st Clement, and the Polycarp's Epistle to be of great worth.

Clement of Alexandria had a similar attitude to the 1st Clement.

And in the book "The Apostolic Constitutions", in the chapter named "The Canons of the Apostles", both of Clement's epistles are listed among the "sacred books of the New Testament" as it says there, and the list of books is attributed to the Twelve Apostles themselves:


  
  Let the following books be esteemed venerable and holy by you, both of
  the clergy and laity. Of the Old Covenant: the five books of
  Moses—Genesis, Exodus, Leviticus, Numbers, and Deuteronomy; one of
  Joshua the son of Nun, one of the Judges, one of Ruth, four of the
  Kings, two of the Chronicles, two of Ezra, one of Esther, one of
  Judith, three of the Maccabees, one of Job, one hundred and fifty
  psalms; three books of Solomon—Proverbs, Ecclesiastes, and the Song of
  Songs; sixteen prophets. And besides these, take care that your young
  persons learn the Wisdom of the very learned Sirach. But our sacred
  books, that is, those of the New Covenant, are these: the four Gospels
  of Matthew, Mark, Luke, and John; the fourteen Epistles of Paul; two
  Epistles of Peter, three of John, one of James, one of Jude; two
  Epistles of Clement; and the Constitutions dedicated to you the
  bishops by me Clement, in eight books; which it is not fit to publish
  before all, because of the mysteries contained in them; and the Acts
  of us the Apostles
Not many direct statements about the lack of canonization of those books were made during the specified time. But a few statements were made.

The canon list in the Muratorian Fragment, dating to about 170, mentions the Shepherd of Hermas, saying that it "cannot be read publicly to the people in church" because "it is after [the apostles'] time":


  Hermas wrote The Shepherd very recently, in our times, in the city of Rome, while bishop Pius, his brother, was occupying the chair of the church of the city of Rome. And therefore it ought indeed to be read; but it cannot be read publicly to the people in church either among the Prophets, whose number is complete, nor among the Apostles, for it is after their time.


That's the only statement I could find that mentions a specific book of the Apostolic Fathers and gives a specific reason for its exclusion from the canon. But I'm not going to end the answer there.

Eusebius, the fourth-century church historian, has four categories of books:


"recognized," which seems to mean that there is a consensus that they belong in the canon
"disputed," which seems to mean that a majority recognize them but some dispute their canonical status
"spurious," which seems to mean that most don't count them as canonical
"heretical," which means that nobody in the church has ever regarded them as trustworthy


About the heretical books he says:


  To none of these has any who belonged to the succession of ecclesiastical writers ever thought it right to refer in his writings. Moreover, the character of the style also is far removed from apostolic usage, and the thought and purport of their contents are completely out of harmony with true orthodoxy and clearly show themselves that they are the forgeries of heretics. For this reason they ought not to be reckoned among the spurious books, but are to be cast aside as altogether absurd and impious.


From this we can infer that Eusebius' criteria for considering a book canonical is that it 1) is accepted by the church, 2) is orthodox, and 3) is from the time of the apostles. He regards Barnabas, the Didache, and the Shepherd of Hermas as "spurious," but doesn't mention any other of the Apostolic Fathers.

Athanasius seems to have a threefold categorization:


Canonical. "These are fountains of salvation, that they who thirst may be satisfied with the living words they contain. In these alone is proclaimed the doctrine of godliness. Let no man add to these, neither let him take ought from these."
Good non-canonical books. "Not indeed included in the Canon, but appointed by the Fathers to be read by those who newly join us, and who wish for instruction in the word of godliness."
Apocrypha. "They are an invention of heretics, who write them when they choose, bestowing upon them their approbation, and assigning to them a date, that so, using them as ancient writings, they may find occasion to lead astray the simple."


Of the Apostolic Fathers, Athanasius only mentions the Didache and the Shepherd of Hermas, both of which he places in the middle group.

Rufinus says that "the ancients" "were willing to have all these read in the churches but not brought forward for the confirmation of doctrine," referring to a handful of books including the Didache and the Shepherd of Hermas, though he doesn't mention any other Apostolic Fathers.

The word they were all using for canon can mean "rule" or "standard" or "measuring stick."

So, although the direct evidence is relatively scant, we can infer the following from the aforementioned facts:


Anything not from the apostles' time was disqualified (which disqualifies most of the Apostolic Fathers, although some of them, like 1 Clement and the Didache, may have been written while John and others were still alive.)
Anything that misrepresented its authorship was out (which probably only disqualifies the Epistle of Barnabas, 2 Clement, and the inauthentic Ignatian epistles.)
The canon was to be the final appealed-to doctrinal word (Athanasius and Rufinus are the clearest expositors of this point, but the word "canon" itself seems to be a clue to this fact.) Jesus, Paul, and John are probably the clearest New Testament examples of speakers/writers who claim to be speaking directly from divine revelation. Perhaps 1 Clement and the Didache, which I mentioned in point 1 as possibly from the apostles' lifetime, were excluded for consciously being doctrinally dependent on the apostolic writings. But that's speculation.
Consensus. Eusebius and Rufinus both seem to believe that the most important canonical criterion is whether "the church" through the ages has accepted the book as fitting the other three criteria. Perhaps the councils were able to make their choices because the consensus had already solidified by that time.