Oops...batch edit mistake. D'oh!!!
Using Jamroom
When you change the field it just changes the field - but there's always more to it than that ... a lot of times items are "ordered by" these fields, and if you empty it then it no longer is "seen" in the list (since there is not a valid value to order by).
Instead of REMOVING the value, you need to change it to "0". I've just done that for you in your DB - reset caches and see if your group is back.