Now that you know it's pasty butt, skip the mineral oil. Is your brooder temperature warm enough? Do they huddle together under the heat source (too cold) or spread out comfortably a little away from the heat source (perfect.) Cold will stress them and cause pasty butt, amongst other things. Make sure there are no breezes chilling them. Clean those affected butts GENTLY, check them every few hours, and don't pull stuff off their vents; soak it gently with warm water and a q-tip until it softens and comes off. If you pull, chances are good skin will come off with the poop, and they will have scar tissue, which doesn't stretch. Not good. A tiny bit of apple cider vinegar in the water (don't use any vinegar if your water dispensers have metal) might help. Keep the bedding and food and water meticulously clean. Watch for pasty butt for another two weeks. Get a powdered probiotic and add it to their feed. Make sure they are on a proper diet for ducklings; the wrong protein level and they can develop "angel wing" deformity. Poultry feed is NOT suitable for ducklings. Good luck with your babies; I hope this all turns around quickly for you, with no more deaths.