Well, personally I think secrets rarely stay secret- sorry. Have seen lots of affairs that are considered "secret", usually ending in disaster.
If I'm honest (and I'm not going to be outraged or indignant, because it's never happened to me, and I understand that wasn't the purpose of the thread) I think it is a cowardly way to deal with things. My friend's wife had an affair, got found out, left with OM, and has been battling ever since to get her dc to speak to her- they will never forgive her for her deviousness, although they may well have forgiven the fact that she fell out of love with their father. They all opted to stay with their dad, which seemed to surprise her. Now, i'm not saying he was a saint- noone can know what goes on in a marriage except the 2 people in it, and I dare say he wasn't the best partner, in terms of affection or romance, but for the children, she will always be the bad guy, because she is the one who deceived and lied.
That one reason alone is enough to put me off the whole idea for ever. As it happens, I wouldn't do it anyway, and am happy in my relationship, but I couldn't damage my relationship with my children for any man