Whether adultery is or is not a forgivable sin depends on who is expected to do the forgiving. It certainly is forgivable by Almighty God, assuming of course that there is sufficient repentence. On the other hand there is no more serious affront to a spouse.
If, in fact, one goes through a religious ceremony and takes the marriage vows seriously, then he/she are agreeing that two become one. Of course this is a metaphor and involves emotional attachment as much as physical. The fact that it is a metaphor does not lessen the degree of pain caused when the vows are broken and adultery is committed.
There have been few divorces in our family, even our extended family, to draw upon for data to answer this question; however the few there have been all resulted from adultery. In two of the cases it was the wife who erred. Neither was remorseful or repentent. In both cases the husbands would have taken them back (there were children involved) had there been remorse. Both women felt justified. One told her spouse that he just wasn't man enough for her. The other told her husband that all the other girls that she hung with were doing it. Both of these women were totally surprised when the husbands filed for divorce. Needless to say, forgiveness was not forthcoming from their spouses or the families of their spouses. Actually, their own families were unforgiving.
Both of these women fought tooth and nail in court hoping to gain financial support in spite of their wrongdoings. Fortunately, the courts have matured in these areas and no longer always find for the men. Both men have custody of the children and do not have to pay "spousal support". Now that they have moved on with their lives, they are finding forgiveness for the two women; however, when they were still emotionally involved, it was devastating to both men.
This indicates that it is not always the male who performs acts of indescretion. Women are ooften more emotional creatures than men. When they are "sinned" against by their partners, it can be overwhelming. Often reason vanishes. They either get so irate that they determine to strip the men bare financially and otherwise. An opposite reaction is dropping into despair. Depression is difficult to deal with. This often occurs because they count themselves as failures who were unable to hold the interest of a husband. Women often manage to blame the other woman rather than their spouse. This makes the indescretion easier to forgive.
A lot depends on whether this was a "one night stand" or an affair. A one-time transgression is much easier to forgive than multiple ones, whether with one person or more than one. I know of an instance where a wife went to be with her family after her brother committed suicide. She stayed for three months, leaving her husband home to care for the children and maintain his business. During that time, he became really lonely and had a one night stand. Eventually they were able to work it out, and she accepted some responsibility for why it happened and forgave him. Another friend discovered a long term affair that her husband had with an employee. She was never able to let it go or to forgive him because to her it was not just sexual, but was a relationship. This cut deeper.
Scripture does name adultery as an acceptable reason for divorce, but it does not say that a spouse must divorce the offender. The New Testament teaches turning the other cheek. If one is strong enough to do that, then yes, adultery is a forgivable sin. This is a very individual thing, but at least today people do not have to stay together "in spite of" whether one is repentent and one is forgiving or not. There are far more options now than ever before with women being able to have careers and support themselves and with the courts being more reasonable in custody of children.