During the EVA inside the sphere Mayweather is seen in the shuttle wearing his standard uniform. Because the shuttle has no airlock it would need to be depressurized to open the door. Mayweather would need to wear some kind of pressure suit. Even if the shuttle could be re-pressurized after the others are out he would need to keep the suit on in case the away team suffered an accident and needed to get back inside quickly. For this reason they would almost certainly keep the door open.
When Trip enters the Med Bay for his pulled muscle, the automatic doors bounce back open as they close. It is curious why they didn't just put doors from a grocery store.