I don't know if there is anything on the Bulletin Board software side which can be done to prevent thread starters deleting threads without admin input, but I expect it is just something we have to live with.
A look at the FAQ section, under "Can I edit my own posts?", suggests that the software can be so altered:-
If you have registered, you will be able to edit and delete your posts. Note that the administrator can disable this ability as he desires. Your ability to edit your posts may also be time-limited, depending on how the administrator has set up the board.