That's an interesting question, and I would say no. That's definitely the case for OBOS, their mission is to disseminate information on and advocate for women's health, which unfortunately is still an ongoing mission.
I'd say instead that the approaches that nonprofits (history or otherwise) take to fulfilling their mission needs to change, as society changes. In OBOS's situation, their mission was primarily fulfilled through print publications, and they realized that today, people are more often getting their information from non-print resources, and when their own digital campaign failed, they realized their approach to their mission was no longer effective. Instead of trying to keep afloat a structure that was no longer working, they acknowledged other organizations doing the same work but better, and are in the process of adjusting their model so they can better support those organizations.
All of this is to say, it's not an issue of whether a history nonprofit can completely accomplish/complete their mission, it's an issue of how nonprofits are approaching their mission, which nonprofits are doing that more effectively than others, and which nonprofits are the most equipped to change with the times.
RE: Bodily Death: Recent News from Our Bodies, Ourselves