The door is called a "wier" or " skimmer" and it's job is to skim off the surface of the water. That removes floating things, such as oil, fine dust and pollen, rubber duckies and small children before they can sink to the floor of the tub where they are harder to clean up. In the case of oil, it works to keep the waterline down to a minimum.
It works! I have had showroom floor models in which we put the water just a bit higher than normal (to make the tub look better/deeper) and it stopped the skimmer wier from working. Those tubs had an oily waterline every morning from the people who stick their lotion-covered hands in all day. We dropped the water level back to normal, the wier was able to do it's job, and the waterline went away.
The thing can get sticky, in which case simply cleaning the track out will get it back to work, but in your case your tub is so new that I think the dealer ought to help you out with a new one.
