[Ronzi]

The previous owner was probably in the habit of lowering the top without executing the "chop" maneuver, i.e. lowering the top part way, then getting out of the car and pressing down the little peak in the plastic that invariably forms pretty much right in the middle of the window.
Big pain in the tailfeathers to be sure, but it is about the only way to prevent long term damage to the window, and ultimately a split in the plastic.