Innovation is absolutely critical for a healthy organization. Without it, decline will set in but not necessarily for the reasons you might think.
Innovation is first and foremost a means of helping people think outside of their current paradigms. It is our paradigms of the way life is and the way we do things that gives us a sense of stability. It is also what keeps us from growing because things don't stay the way they are, our world changes around us and there is always someone who is bent on doing what we do better than we do it.
General Motors learned this well after Toyota had eaten their lunch. Churches learn this when they lag behind and find that their people have moved on. Non-profits learn this when others find better and more cost effective ways of doing what they do and their donors move to the more efficient way.
Those left behind have many ways of explaining their loss but usually their explanation points to external forces rather than where the true reason lies - themselves and their old paradigms that have been eclipsed.
How do you keep this from happening? You create a culture of innovation where new ways of doing old things can keep your staff from becoming rigid, inflexible and content with what was but not what will be.
Innovation fosters thinking that is outside the traditional box. It fosters better and new and less costly ways of accomplishing what your mission says you are about. It literally changes the mindset and thinking of your staff. They become more flexible, ask better questions, never assume that the way they have done things is the way to do them today and continuously create new ways of doing what they do. It fosters better and more strategic thinking!
Organizations that don't innovate regularly become lazy and their paradigms stultified. Those that do stay on the edge of opportunity and and success.