Forgiving the person who has cheated usually leads to only one outcome.

After many people suffer betrayal, they are reluctant to let go of their years of affection and the past companionship, and choose to easily forgive the cheating partner. They always believe that the other person will correct their mistakes and sincerely repent, and will cherish themselves more and manage the relationship well.
However, the reality is often contrary to their expectations. Easily forgiving the betrayal usually leads to the second or third round of hurt. Human nature has a tendency to take chances. Once a mistake is easily tolerated, one will assume that the cost of making the mistake is very low and there is no need to pay a price. Then they will repeatedly test your bottom line.
Temporary remorse, sincere apology, and tearful persuasion are mostly just temporary compromises, not true repentance. Unconditional forgiveness does not lead to true repentance; instead, it will make the other person more reckless and disregard your sincerity and bottom line.
There should be a limit to tolerance in relationships, and kindness should have a sharp edge. There are only zero and countless times of infidelity. Easily forgiving will not lead to long-term cherishing. Taking timely action to stop and leaving gracefully is the best way to protect yourself and avoid secondary harm.