Why would the professor want to prevent the students from continuing? What's wrong with it? If they continue to discuss the on-topic stuff even after the obligatory period, it means they have become interested. Why would this be undesirable?
However, if there are good reasons for that, you might (after the deadline) edit the forum properties and set them to "no discussions, no replies". All messages posted to date will be archived and accessible to the students, but they won't be able to post any new messages.