You can feel this when playing fast and loud, with thick texture, large chords and all the stops of the organ. The impression is that the organ has a difficult time breathing. The bellows, by the way, are often called the lungs of the organ not by accident.
What can you do in this situation?
1. Avoid using stops which require a lot of air but add little to the general loudness of the organ - 16' and 8' flutes.
2. Avoid doubling stops of the same pitch level.
3. Avoid using manual couplers.
4. Some of the chords can be played and released not entirely together.
5. Choose a different piece.
Sometimes the impression that the organ lacks air comes not necessarily because of the defect in the wind supply system. It may be entirely possible that this is simply a part of the organ style.
We must remember that many Baroque instruments have quite low air pressure in the bellows. Because of this, the Romantic or symphonic music sounds unnatural on such organ. In this case, better choose a piece which suits the style of such organ.
Don't fight the instrument. Simply let it play.