Which church had a reputation for being alive, yet was dead?

Answer: Sardis

To Sardis: "I know your deeds; you have a reputation for being alive, yet you are dead."

““To the angel of the church in Sardis write: These are the words of the One who holds the seven spirits of God and the seven stars. I know your deeds; you have a reputation for being alive, yet you are dead.”— Revelation 3:1 (BSB)