Any board member, or potential board member, should go through a similar cycle as a potential donor (and all board members should be donors!). A period of getting to know each other should be followed by a decision to continue a relationship based on the resources that are needed and the resources being offered. For the most part, board members are very well-intentioned people. They want to serve their community.
Is your board supporting your organization in a way that helps your nonprofit or are they diverting resources with pet projects and off topic ideas? Clear expectations, roles and responsibilities should be communicated to potential and current board members. Your organization should consistently be looking for new board members, consider term limits and maintain a level of morale that permeates your entire organization. The board and you are the rudder of the ship - make sure you plan to steer them in the best direction.
As the administrative leader of your organization you should be providing stewardship to your board members. Make sure they know their time and talent is needed and valued by you and the organization.
Once a year you should host a board retreat. It doesn't have to be fancy (and probably shouldn't be) - but it should be upbeat, fun and purposeful. It should be an opportunity to thank your board members and reignite their passion for the mission.