_S_1_M_0_N_ the exact logic is described in more detail in these posts: SKevo, SKevo, and also in the documentation.
Note that since then, the logic might've changed a bit, but I referenced the posts anyways so you can understand the mechanism better. But the current logic is: if admin account was last seen before 2 months, the forum is inactive.
However, this logic will be changed again - I am considering to just keep it simple, such as "if less than 2 posts, it is unused" in the future, as the current system is not very reliable in some edge cases (for example, admins not using the main admin account - which is discouraged, but well, it happens)