And for many nonprofit groups, survival these days depends more on a savvy manager who can secure competitive grants and government contracts than on attracting small donors. Private donations make up about 10 percent of the funding for nonprofit agencies, said Rick Cohen, of the National Council of Nonprofits.

"Individual giving has rebounded a bit, but state and local governments are still in the midst of the recession and in the midst of budget problems," Cohen said. "A good leader makes sure that the resources of that organization are deployed as effectively as possible. That's part of why it's important to get the right leader in and make sure you can keep that leader."