I could be wrong, but I think that was a Daewoo prototype that never saw production at all (not even in Korea.) It really is a shame because its very cute and probably would have sold well (at least in California where I live.)
The only problem with convertibles (from a production standpoint) is that they are generally money-losers. They are expensive to manufacture and require the frame to be reinforced (cutting off the top greatly reduces structural integrity) and complicated top mechanisms. They also don't generally sell very well.
The generally arguement in favor of convertibles is that they are an "image booster." They make a line of car seem sexier/funner. For instance, if Daewoo had created a convertible model in the US, Lanos says would have increased across the board because people would look at the Lanos convertible and say "wow... that's cute... well, I can't really afford (or don't need) the convertible model, but the 3 door is nice..."
Generally poor decisions that led the company to financial troubles combined with the fact they waited too late to release such a car. They tried to emulate GM and would up getting taken over by them!