The only time I believe in giving up on a marriage is when one of them dies, or if after their divorce one of them marries someone else, or if one of them continues involvement in an activity that makes the marriage impossible. Otherwise, I believe there is a chance to reconcile.
The first two death or one of them marrying someone else are obvious. I will briefly explain the third. When someone asks me if they should make the effort to save their marriage when their spouse has done some bad thing I always ask, "Is your spouse a good person doing a bad thing, or a bad person doing a bad thing?" The intention of the question is whether beneath the current bad behavior there exists a good heart or if the person is so intent on his or her selfish behavior there is no chance to rescue them. Judging a person by what he or she is doing now can sometimes lead to the wrong conclusion.
That said, there are actions that make it impossible for a marriage to continue. Here are a few examples:
If one continues in an affair, even after confrontation, it is impossible for the other spouse to continue to live in that marriage. (Though I use the word "impossible," I know of some who have. I don't recommend it.)
If a person is abusing his or her spouse or children, remaining in that marriage is unwise. Abuse may be physical, sexual, emotional, or a combination thereof. I have seen marriages reconcile after the abuser got proper help, but even then strict boundaries were put in place to ensure that no more abuse could occur. If the abuser does not seek or accept the help he or she needs so that their bad behavior is corrected, living with them is not a viable option.
The example list could go on. Sometimes the unhealthy, bad behavior of a spouse makes it treacherous for spouse or children to remain in the same home. If a person refuses to stop the devastating behavior, that person eventually becomes unbearable to live with.
However, allow me to point out that there should be patience in concluding that a person will not stop the action destroying the marriage. Often a planned intervention works and can help to rescue a straying spouse.
Before giving up on a person, have the grace and mercy to try all that can be done to rescue them. Thats why I always encourage a spouse about to end a marriage to seek wise counsel to determine if the spouse is truly hopelessly involved in his or her actions. Hurt and angry spouses sometimes make judgments about their spouses that may be incorrect.
If a person can be rescued, they should be. If a marriage has any chance of reconciliation, that chance should be explored to the deepest level.