The emotions that come with a relationship are often what can hold a couple together when one of them has betrayed the other. The actual betrayal is less important than the fact it was done. Whatever issue a couple faces, giving a partner a second chance shows a willingness to succeed as a couple. Working for relationship success should be the main goal of the person who caused the break in the first place. Their new job is to maintain their relationship as they find ways to improve their own behaviour.
Accepting responsibility for what they have done is often the reason a betrayed partner is willing to give a person one more opportunity to continue their relationship. It is a gift that few people may be able to afford these days, and it should be viewed in that way. For those trying to straighten out their life and relationship, remembering that they have been granted that gift can be what pushes them to succeed in the relationship.
Cheating or addiction are often the reasons a couple splits up, and overcoming the pain it causes does take time. A partner that has been betrayed in this manner will usually be hurt and angry. Recognizing these are valid feelings they should have is part of accepting responsibility. It may be difficult to put up with being blamed and dealing with the anger, but the opportunity to continue the relationship should be the foremost consideration.
Getting past what has happened generally takes more than just a few weeks or months. The person who has been wounded may say nothing much at first, but bursts of anger can be a result over time. Learning to deal with that anger and accept it as a part of the healing process can be a road to recovery for both partners.