I may have butchered the quote a little bit (not a famous quote, just something told to me once).

"If you spend too long convincing someone of a problem they can't see, they start to see you as the problem" gets the meaning better. It doesn't mean to give up, it just means that you are making yourself their enemy and thus probably making it harder to get your message across (look at the studies on showing scientific evidence to anti-vaxxers).