In Ephesians 4:11-14, Paul said (regarding Christ): "And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers; for the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ: till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ: that we henceforth be no more children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, and cunning craftiness, whereby they lie in wait to deceive
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Jesus Christ built His Church on a foundation of prophets and apostles. As Paul explained, this organization was to exist until we all come into the unity of faith. To the best of my knowledge, we're not there yet! There are over 30,000 different Christian denominations in existence today. Why? Because the organization of the Church Christ established ceased to exist. What happens to any structure if the foundation is removed? Obviously, it crumbles and the structure it was supporting can no longer stand. Without living prophets, even those who are completely sincere in wanting to follow Jesus Christ don't know exactly what to believe. They are, as Paul said they'd be, like "children, tossed about by every wind of doctrine."
There is absolutely nothing in the Bible that can be used to justify the belief that a living prophet is no longer needed Christ's Church -- exactly as Peter led it in the beginning.