Yeah I have had a ship design just completely disappear also, right after the shipyard built the first one of that design.
As far as the obsolete and delete goes: Obsolete lets you remove a game designed ship from the lists, for the remainder of your current game (although this is bugged at the moment). It will be back when you research the techs needed in your future games. Delete lets you permanently remove one of your own designs you don't want anymore.