The Early Church Fathers demonstrate that the gifts did continue, but their necessity faded as time went on. I recommend reading St. Gregory the Great’s Dialogues, he gives many examples of miracles that happened in his own time.
The need for certain gifts were greater early on, because the Lord’s main purpose was to spread the Gospel. The gifts in themselves were not important compared to the results of those gifts, and that was to establish the Church world wide. The gifts of tongues were needed in order to speak to all people with different languages. Healing was important in order to enhace the faith of those being preached to. Prophecy was needed in order to help teach a faith that was new and demanded supernatural proclamation. But as the Church grew abundantly, the evidence of a vast Body of Christians who devoted their whole life to Christ, with the power of the Gospel message, the NEED for those gifts for the sake of spreading the Gospel was needed less and less. As Bishops and priests were being appointed in all regions and in different languages, the gift of tongues was not needed as often. And the momentum and growth of the Church, which is a convincing evidence in itself, the need to amaze people with great miracles for the sake of faith was not needed as often. The establishment and organization of the teaching office of the Church, the need for prophecy the way it was early on was needed less. But the gifts that we see in the New Testament still happen and are not dead, but their purpose of bringing people to faith is less needed.
