Men and women are sinful, Kay Cee. If either partner decides to leave, and seek a divorce, and does so in rebellion to God’s Word, after the disciplinary steps of Mt. 18:15-17 are exhausted, then the one who will not repent is to be treated as an unbeliever, and, as such, he or she has deserted the other partner, and a divorce will be granted on the basis of 1 Cor 7:15.
At my church, that is a grave matter; after the initial steps of Mt 18 are exhausted, an announcement is made before the whole church that so and so has abandoned his or her spouse, and has refused to repent. At that point, those who know the unrepentant party are encouraged to appeal to him or her, and urge them to reconsider their decision, and to repent of their sin; sometimes they do repent; at other times, they do not repent.
Only God can change the rebellious heart. According to 1 Cor 7:15, the faithful spouse is not under bondage to the unbelieving spouse, as determined by Mt 18:17, ie., the unfaithful spouse is to the faithful spouse, and to the church, a Gentile, and a Tax-Collector, re: an unbeliever who will not repent.
The faithful spouse may wait for the unfaithful spouse to repent for as long as he or she will, but if the other will not repent, and initiates and demands a divorce, what else can be done?