You can forgive and choose to stay yet it's really hard to forget... I think if it happens, you will always have that feeling that he/she might be cheating on you again...

I think some salvage the relationship for various reasons,. there's their children, their marriage or family image, political career, financial security, love(?) etc..

IMO, if i am not married yet, i will surely (no doubt!) let go, but if i am already married, I "might" have a different decision.