Much effort is exerted to get someone to "like" your Facebook page. Equal or greater effort is needed to earn a return visit.
Businesses and organizations spend a lot of time and money to accumulate a large number of followers. But if you don't give them any reason to follow you closely, it is a paper army.
People, even your most devoted fans, are busy. They will only return to your Facebook page when there is a reason. Giving them a good reason is your challenge.
Contests and events attract interest. So does quality content that informs or inspires. Best of all is some type of engagement, in which you ask for their ideas or involvement. Blogs routinely trot out lists of things to do to bolster your Facebook ranks and keep them excited. In truth, there isn't a formula for success. Each brand, organization or cause needs to find its own sweet spot.
A contest may be inappropriate to raise awareness and recruit financial donors for a cause. Events may be impractical for certain kinds of products or services.
What brings people back, including fans, is engaging content of interest to them. If you are in sync with your target audience, that may seem like a natural expression to you. If not, you need to talk to your fan base or potential fan base to find out what they like about you and what they want to know more about.