Good question... and one that I don't have a good answer for.
As a Christian I believe that I am "right" when what I say is in agreement with what scripture says. Otherwise, I give myself maybe 50/50 odds...
Anyway, yeah, if the other person isn't a Christian there's little to no common referance as to correctness, and both can be equally assured that they are the one in the right.
As an ex- Sunday School teacher, and in life in general, I have to remind myself that I can't expect non-Christian to live up to Biblical expectations. They just don't mean anything to them...
To answer your question as to how many times... well, it depends on the person(s) and the subject. Usually when I realize that it's getting nowhere, that I won't change their view no matter what I say, or when I'm deciding to beat my own head or theirs against the wall is when I call it done. At least they've heard my view on things, for whatever worth they consider it, and I always at least try to "discuss" in a way that isn't overly aggressive, in the hopes that I can always talk with them again. Sometimes that works, sometimes not...
God Bless
Kevin