The apostasy hadn't occurred yet in Polycarp's time - to the contrary, church persecution was so intense at that time that it protected it from apostasy. But after 321 A.D., when Constantine opened the way for the co-mingling of truth and error, the apostasy really started taking hold.
Paul said "after my departure wolves will come in"
Acts 20
28 Be on guard for yourselves and for all the flock, among which the Holy Spirit has made you overseers, to shepherd the church of God which He purchased with His own blood. 29 I know that after my departure savage wolves will come in among you, not sparing the flock; 30 and from among your own selves men will arise, speaking perverse things, to draw away the disciples after them. 31 Therefore be on the alert
1 Tim 1
3 As I urged you upon my departure for Macedonia, remain on at Ephesus so that you may instruct certain men not to teach strange doctrines, 4 nor to pay attention to myths and endless genealogies, which give rise to mere speculation rather than furthering the administration of God which is by faith. 5 But the goal of our instruction is love from a pure heart and a good conscience and a sincere faith. 6 For some men, straying from these things, have turned aside to fruitless discussion,
Jude 1
3 Beloved, while I was making every effort to write you about our common salvation, I felt the necessity to write to you appealing that you contend earnestly for the faith which was once for all handed down to the saints. 4 For certain persons have crept in unnoticed, those who were long beforehand marked out for this condemnation, ungodly persons who turn the grace of our God into licentiousness and deny our only Master and Lord, Jesus Christ.
3 John 1
9 I wrote something to the church; but Diotrephes, who loves to be first among them, does not accept what we say. 10 For this reason, if I come, I will call attention to his deeds which he does, unjustly accusing us with wicked words; and not satisfied with this, he himself does not receive the brethren, either, and he forbids those who desire to do so and puts them out of the church.
Your contention that almost 3 centuries later "still pure as the driven snow" is not entirely supportable from the actual text of scripture.
2 Thess 2 reminds us that a great "falling away" a great apostasy in the church was coming.