The topic of cheating is always a facinating one, with its plethora of variables.
I tend to agree with Fancy and others on the fact that unless the other party was totally unaware of the cheater being in a relationship, equal blame should be cast on both.
The cheated on spouse, especially when female, tends to blame the other woman because of an expected 'loyalty' between women to leave each other's men alone, and therefore feel much more disgust, betrayal and resentment for the other woman. -one could say those feelings are misguided, but then would fall victim to alledging that women have no loyalty to one another.
Back to the topic, the reasons why the cheated on spouse would want to stay in the relationship, do depend on the individual.
Some just cannot forgive and forget, the reasons for which vary from past hurt to personal choice.
The level of self-doubt that goes through a person's mind cannot be fathomed by those who've never experienced it. A common question that runs through one's mind would be: why wasn't I enough for him/her?
Many feel they've given so much of their lives and energy to a relationship that they: can't handle being single and out there again, can't bear to feel like a failure, or genuinely believe that such behaviour was momentary and shan't happen again.
Whatever the reasons, it's never good to judge or make someone feel guilty for going back to the relationship. However, if they do decide this, it's imperative that they have a long, serious evaluation and discussion of what they need in order to attempt regaining trust.
The worst mistake people make, and very often the reason the person cheats again, is because things just carry on as they were, or go back to normal. Normal clearly wasn't working, and therefore a way forward should be established with restrictions.
What would I do? Well, I could say that I would never be in such a situation, but that would be presumptive and statistically unlikely. In my present demeanour, I would probably not carry-on with the relationship, but then again I'm not in one, so it's easy to say that without the emotional involvement.
My best advice is to do what's best for you and remember that both decisions have consequences.