One way to regain their influence is to research and put up strong candidates. When I say strong candidates, it is not enough to have a great voting record, or positions/platform. They need to be able to articulate their conservative positions with a reasonable degree of skill, they need to be able to handle media and scrutiny, and most of all they need the ability know what to say and what not to say. The goal is to win as many votes as possible with sacrificing your principles.
Research the candidate is key in that there are no big surprises in their backgrounds.