From a technical point of view, it would be difficult to backup a site like the SAB forums without the co-operation of whoever has admin rights on the server that hosts the forum.
You could certainly write a script (robots!) to navigate each forum thread and save it out to a static HTML document, but you'd lose all the forum functions in the process (like, making new posts, or viewing a members profile, or changing your name etc).
That would be great as a static archive like the Way Back Machine but not so great to keep the forum 'alive'.
*If* you had the co-operation of the server admin - moving the forum, or creating a copy / backup, would be relatively simple.
I guess the question is: who would pay the bill for the new hosting, who would do the tech support and who would compensate Torsten for the years of work and resources he's poured in to this place?