Jesus never "reinstates" anyone." Have you ever heard of anyone being "unborn"? And then having to be born again and then again? No such concept is found in the Bible.
Matthew 26:33 Peter replied, “Even if all fall away on account of you, I never will.”
Matthew 26:35 But Peter declared, “Even if I have to die with you, I will never disown you.” And all the other disciples said the same.
John 13:37 Peter asked, “Lord, why can’t I follow you now? I will lay down my life for you.”
John 13:38 Then Jesus answered, “Will you really lay down your life for me? I tell you the truth, before the rooster crows, you will disown me three times!
Mark 14:30 “I tell you the truth,” Jesus answered, “today—yes, tonight—before the rooster crows twice you yourself will disown me three times.”
31 But Peter insisted emphatically, “Even if I have to die with you, I will never disown you.” And all the others said the same.
Mark 14:72 Immediately the rooster crowed the second time. Then Peter remembered the word Jesus had spoken to him: “Before the rooster crows twice you will disown me three times.” And he broke down and wept.
John 21:7 Then the disciple whom Jesus loved said to Peter, "It is the Lord!" As soon as Simon Peter heard him say, "It is the Lord," he wrapped his outer garment around him (for he had taken it off) and jumped into the water.
Peter was ashamed that he denied Jesus three times.
Jesus said Peter's faith would fail him.
Luke 22:31 "Simon, Simon, Satan has asked to sift you as wheat.
Luke 22:32 But I have prayed for you, Simon, that your faith may not fail. And when you have turned back, strengthen your brothers."
Peter's faith HAD failed him. He was given the chance to turn back, after Jesus reinstated him.
Peter denied Jesus three times, and three times Jesus confirms the reinstating.
John 21:15-19
Jesus Reinstates Peter
15 When they had finished eating, Jesus said to Simon Peter, “Simon son of John, do you truly love me more than these?”
“Yes, Lord,” he said, “you know that I love you.”
Jesus said, “Feed my lambs.”
16 Again Jesus said, “Simon son of John, do you truly love me?”
He answered, “Yes, Lord, you know that I love you.”
Jesus said, “Take care of my sheep.”
17 The third time he said to him, “Simon son of John, do you love me?”
Peter was hurt because Jesus asked him the third time, “Do you love me?” He said, “Lord, you know all things; you know that I love you.”
19 Jesus said this to indicate the kind of death by which Peter would glorify God. Then he said to him, "Follow me!"