Mine too but I have been told it's better to unzip it to put the top down. But to answer op's original question on a hot summer day unzip that back window, roll down all the windows, open the air box, and leave the top up. It keeps the sun off of you and really lets the air flow. It's actually my favorite way to drive my car!
Yes, mine will also go all the way up and down, but unless everything is massaged into place as the top is lowered, there are folds and frames poking the cover. If you don't use a cover, it's fine, but it looks like crap if not tucked in tightly before the cover is installed.