As to the question, yeah, if you're past the point of the reset options, once broken by a bad deed you can't go back to Idolized. You can improve your rep to a point where it's high again (so they won't attack you on sight, say), but the negative still remains on your record, so to speak, and the actual title of Idolized is unattainable...instead you get a "mixed rep" title. It does not take much to drop a rep level, either. Not much at all.