Consider that Peter denied Christ THREE TIMES when confronted by the Jews............. Christ posed His question THREE TIMES to Peter........ Not a coincidence IMO........
Not sure what the coincidence is though.
Peter denied Jesus out of fear and weaknesses.
Part of me wonders if his response to Jesus asking him if he loved him whether he felt guilty.
After all just before the arrest of Jesus we see Peter saying
Matthew 26:35
35 “No!” Peter insisted. “Even if I have to die with you, I will never deny you!” And all the other disciples vowed the same.
Luke 22:31-34
Jesus Predicts Peter’s Denial
Luke 22:31-34; cp. Matt 26:31-35 // Mark 14:27-31; cp. John 13:36-38
31 “Simon, Simon, Satan has asked to sift each of you like wheat.
32 But I have pleaded in prayer for you, Simon, that your faith should not fail. So when you have repented and turned to me again, strengthen your brothers.”
33 Peter said, “Lord, I am ready to go to prison with you, and even to die with you.”
34 But Jesus said, “Peter, let me tell you something. Before the rooster crows tomorrow morning, you will deny three times that you even know me.”
I don't think Peters faith failed, just his love.
His love then moved from Phileo to Agape.