Have you ever watched the HBO series The Wire? One of the things I like most about that show is that the writers kill off the characters when it makes sense for the story, not when the audience gets tired of a character. In the last season, they killed off one of their strongest, most popular characters, and the impact was huge. What the writers are doing is keeping the story real, compelling, and moving forward by introducing new plots, new characters, new twists – not by hanging on to beloved characters that should have be killed.
My advice: stay true to your story, not your characters. In the end, it will be keeping true to both.