If people reject Jesus long enough, will he turn away from them?

In Mark 6:11 and Luke 9:5, Jesus instructs his disciples to shake the dust off their feet against a town if the people refused to hear the message.  In Matthew 23:37, Jesus laments Jerusalem’s rejection of him:  “O Jerusalem, Jerusalem, you who kill the prophets and stone those sent to you, how often I have longed to gather your children together, as a hen gathers her chicks under her wings, but you were not willing.”

Jesus is clear that people have rejected either him or his disciples.  It is inconclusive to say that those towns will no longer have an opportunity to respond to the Gospel.  However, the cities of Sodom and Gomorrah were often used as examples of ultimately rejecting God and receiving ultimate judgment.

In short, if God knocks, answer the door.  We are not promised another second of life.