The dust must be getting inside via the vertical gap between the glass panels. If your home is very breezy, even a tiny gap is enough for dust to filter through. Stop the dust from entering by adding a second line of defence – a strip of soft rubber seal attached to the inside of one glass panel. Position the seal so it bridges the opening.
You can find these thin rubber or brush strips (called flanges) in DIY shops. They can be secured to the cabinet door frame using glue or small nails.