The threads don't disappear, they just don't show themselves after a certain period of time - but you can still see them.
When you're in a forum looking at the list of topics you may notice a drop down menu a little below the words 'add topic'. It says 'show topics from last 60 days' or something (I think 60 days is the default). You can choose 'show all topics' from the menu.
If you want to change the number of days that you see for all the forums, you can change this in your preferences (again - just below 'add topic').