Though I don't think the forum will ever shut down, it's possible. In case the forum shuts down, it won't hurt Bitcoin anyway. Because the forum is for learning and discussion purposes, it isn't related to Bitcoin directly. Most probably anyone could create another forum again, same like Bitcointalk, if this forum shut down for some reason. So far we can see the forum admin is very careful to run this forum smoothly. Even he is complying with regulations, like banning all the mixer-related campaigns and threads.

Bitcoin already found its path, so it will run as usual, either the forum alive or dead. No one can stop Bitcoin ever since it's decentralised. Already Bitcoin is gaining popularity worldwide, and big investors are already in. They definitely won't dump themselves; somehow Bitcoin adoption will keep continuing.