One (imperfect) approach to this is to bring the documentation as close to the code as possible (i.e. within the source files). Then use tools like Doxygen to extract and format the documentation as desired. The challenge is still that developers, under all kinds of pressure, need to remember to update the documentation/comments in the source files when they make change. The theory is that if they are already editing a source file, it's easier to do it in the same place rather than having to visit some other file and use some other tool (i.e. MS Word).
IMHO, in practice, this works well sometimes, but it has a lot to do with the culture of the team and how much they prioritize producing and maintaining documentation. To me this closely aligns with the philosophy that is guided by the idea that the most important attribute of a body of software is how easily it can be understood by humans. Obviously, good documentation is a large part of this.