By the 3rd century, the spiritual gifts were gone. But they were still there in the early 2nd century.
"The gift of prophecy, while it remained, was the boast and glory of the church. Thus when Justin wishes to prove to a Jewish friend that the truth has now passed from the Jewish to the Christian community, his one argument is that the gift of prophecy, once enjoyed by the Jews, has now been transferred to his own people, the proof of which, he says, is "that prophetic gifts are to be found among us to the present day,... such as were anciently shared among you." "
(The World and the Prophets, Nibley, pg. 4)

Origin later said that there were still "traces" of the spiritual gifts in his day.   But by the time of Augustine, they had disappeared.  

"For not even now, when a hand is laid on the baptized, do they receive the Holy Spirit in such a way that they speak with the tongues of all nations; nor are the sick now healed by the passing shadow of the preachers of Christ. Even though such things happened at that time, manifestly these ceased later." - Augustine

"When the Catholic Church had been founded and diffused throughout the whole world, on the one hand miracles were not allowed to continue till our time, lest the mind should always seek visible things, and the human race should grow cold by becoming accustomed to things which when they were novelties kindled its faith. (Augustine: Earlier Writings, Library of Christian Classics, 248)
"Why, saith one, are there not now those who raise the dead, and perform cures? Yes, then, why, I say: why are there not now those who have a contempt for this present life? Do we serve God for hire? When man’s nature was weaker, when the Faith had to be planted, there were even many such; but now he would not have us to hang upon these signs, but to be ready for death. [...] For this cause it is that there are none such now; because that (future) life hath seemed to us honorless, seeing that for its sake we do nothing, whilst for this there is nothing we refuse to undergo."
(Homily 8 on Colossians)
There seems to be widespread belief that the the miracles and gifts of the spirit ceased with the apostles.
John Chrysostom lived in the 4th century and was constantly explaining to the church members why they shouldn't be upset at the loss of the spiritual gifts.
"Are we today not just as good as the apostles? ...but they had signs and wonders you say. But that is not what made them great. How long will we go on excusing our own indifference by appealing to their signs and wonders? " (Chrysostom, In Matth. Homil., 46, in Patrologia Gracia 58:479)