Is this person at a manager level not working as a manager, or at a more junior level not working as a manager?
Does the job description match the tasks?

OP, I also work at a nonprofit and had an employee who was very similar to this. Our HR department is clueless and provided no guidance. I literally could not figure out what this employee was doing all day long. I eventually gave him a very micromanagey task list that he had to complete each week and report to me on his progress. When he couldn't even get that done, I documented everything and let him go.

In this economy, it's just not fair to the other employees who are working hard to allow one employee to totally slack off-- no matter how much people like that employee.