Part of his success was his personal convictions. He believed in what he thought and would not compromise them. His constituents voted him in because that's what they wanted. Someone who didn't take the easy out and sell out.
Helms' personal convictions, in his own words, can be found in the quotes below. You're right, Ray, Helms "believed in what he thought and would not compromise them." I disagree, though, that he didn't take the "easy out and sell out." He did. The harder path, the truly Christian path (not the perverted version of Christianity he espoused) would have been to recognize that his words were harmful, that he was wrong and to admit that he had been a hateful bigot whose actions in the Senate caused much harm to his constituents (he represented all the people of North Carolina, not just the straight, white ones).
Helms on race:
"No intelligent Negro citizen should be insulted by a reference to this very plain fact of life. It is time to face honestly and sincerely the purely scientific statistical evidence of natural racial distinction in group intellect. There is no bigotry either implicit or intended in such a realistic confrontation with the facts of life."
Helms on Gays and AIDS:
"Nothing positive happened to Sodom and Gomorrah, and nothing positive is likely to happen to America if our people succumb to the drumbeats of support for the homosexual lifestyle."
"The government should spend less money on people with AIDS because they got sick as a result of deliberate, disgusting, revolting conduct."
Now, that didn't make him right on everything- but he was re-elected based on his personality and attitude not his political ideas. although I would admit that many of the folks who voted for him probably did agree with his political agenda.
Ideally, our representatives in the Senate are supposed to represent the best of our hopes and dreams. They are not supposed to, as Helms did, exploit and encourage our worst traits in service of their own naked quest for power. I'm not so naive as to believe this actually happens, but Helms' legacy represents the worst elements of American society and political ambition.