I voted other and wish to explain my opinion:
I think the board will be closed when new posts on the board dwindle beneath a certain monthly threshold. For example, if there is a month when there are only 10 new posts on the board, it's time for it to be closed. (Exact number of posts can be determined, or when mods think we hit that point.)
Now for the unasked question - what to do with the board? Disband it to other boards? Delete it?
I don't know the programming aspect of this, but if it would be feasible, I think a small link should be put at the bottom of DDF called "Dormant Boards," and clicking on it will bring up a list of all dormant boards.