If the Church is the body of Christ, it is a living, growing entity. It is what it is, and unlike anyone of us cannot become something else. Just as Christ did not spring into being like Athena from the brow of Zeus, but was conceived, formed in the womb of the Virgin, was born, and grew up, and fulfilled his mission, so the Church, except that he did what he did without sin, and the Church fails, falters and recovers. But even Our Lord faltered under the weight of the Cross.
Even so, He set the example. He picked Himself up and kept on going to Calvary, where He said: "It is finished".
Amen.
Strictly speaking, the Church does not, in fact cannot, "fail, falter and recover." If you mean popes or people or movements or theological theories or doctrines or priests, etc, yes of course they may change or fail. But there is no distinction between Christ and His Church in terms of moral infallibility. The Chruch's dogma cannot be wrong, as promised by Christ.
Catholism is a living religion, not a religion based on a book, but the Living Word, present in the world as Christ in his Church and through the Eucharist. The revealed truths of God (in His Church) have never altered.