Life is a personal journey.
It's important to remember that there is no such thing as an "Universal Deal Breaker". Whatever you or I could possibly think of there is someone living under those conditions who has no plans of going anywhere!
Secondly as askformore mentioned (circumstances) do matter to most people. One of the main reasons why people who have been cheated on ask the question; (Why?) is because a part of them wants to find a reason to justify staying.
Also oftentimes the shock of learning one has been cheated on and the thought of going through a breakup or divorce all at once is too much to bear for some people. This is especially true if the couple has been together for more than a couple of years. If a couple has children together that may also play into one's decision as to whether to stay and try to work things out.
If the cheater shows (sincere contrition), regret, and pleads for forgiveness coupled with being willing to go into couple's therapy their mate may be willing to give the relationship a second chance if they're "in love" with them.
Last but not least there are some people who know they've been neglectful, taken their mate for granted, stopped having sex or being affectionate. Even though it was the (cheater's) decision to cheat it's not uncommon for a betrayed person to look at some of the "extenuating circumstances"
Having said that sometimes people WANT to forgive so they try to stick it out only to discover that they can't get out it of their mind!
No matter how much their mate bends over backwards, becomes transparent, or demonstrates honesty and integrity moving forward they still resent them and some have been known to do a little "revenge cheating" or simply end the relationship after telling the cheater they (forgave) them!
Suddenly the cheater feels betrayed. Just because one doesn't leave "immediately" doesn't mean they will stay for life.