Is once a cheater always a cheater really true? Not necessarily.
Not everyone who cheats will inevitably cheat again. Otherwise, if we assume, “once a cheater, always a cheater,” we are assuming that out of about eight billion people on this planet, not one has the capacity to change. Not even ONE.
Applying that logic, does that also mean that if you commit a crime, you’re just bound to commit a crime again no matter how much remorse you feel? What about if you were an alcoholic who drank every single day? Does that mean you’re bound to relapse and become an alcoholic again, and again, and again? You see my point. When you really think about it, that doesn't make much sense, does it?
However, in saying this, I do believe cheaters who do change are few and far between because the best indicator of future behavior is past behavior. It ultimately depends on many factors: the person’s values; the person being cheated on (remember, not everyone has the same character traits, and not everyone gets treated the same by every partner), the level of guilt the person experiences after; whether he or she is willing to take responsibility; etc.
Also, not all affairs are equal. There’s a huge difference between a one-night fling and a long-term affair, an affair that drags on for months or years and involves an emotional investment with another person. Some can be overcome, some are virtually impossible. Just depends.
In sum, I don’t think it’s always true, but frankly unless there's some really, REALLY, convincing evidence that it won't happen again, I would not stick around to find out.