Retention is our responsibility, yeah. Realistically, though, it's tough to keep even a majority of the people that sign up. There has been some research on the subject, and even the best "sign up and play" games have a mid-term retention rate of at most 40%, which makes things difficult. True, users that are referred by a friend have a higher likelihood of sticking around, but there is a logical limit to it.
Perhaps we'll need to rethink the tracking of referred users for the page and for this contest, etc.