Jesus is indeed the gift that keeps on giving. No matter how much our sins keep recurring over and over again, God forgives us in the same way, over and over again.
There are some people, however, who, no matter how many times they have been given a second chance, but, for whatever reason, did not accept such chance. There are numerous biblical stories of people who have rejected the second chances given by God.
Jezebel rejected her second chance and deliberately disobeyed God. (2Kings 9:30-37). Bernice heard the gospel message preached by Paul yet there was no indication she accepted it (Acts 25:23; 26: 30-32).
Even though we have temporary consequences in our disobedience, we can still be forgiven and given the assurance of life because our sins are covered by the blood of Jesus. Even after we sin again, there will still be consequences because God's justice allows consequences for forgiven sins but His forgiveness and mercy continues to offer the protection of a gracious and forgiving heavenly Father. It is no different than a loving earthly father who takes away privileges after we have disobeyed him but the love never goes away and continues to forgive us no matter how many times we screw up.
Until my next rant.... LOVE ONE ANOTHER!