You are correct in identifying moisture as the likely culprit for peeling paint. However, unless you fix the probable cause, your next coat will also peel, regardless of the vent's CFM.
Most bathrooms historically were painted with oils, and to prevent moisture from penetrating the paint, I've read that it is probably a good idea to stay in oil. However, whatever finish you apply, 85 to 90% of the work that will ensure longevity is the preparation. You will probably have to start by scraping off the latex paint recently applied; a power angle head grinder with a fine to medium carbide flexible sanding disk will be effective to do this: but be prepared for a giant mess. Once the paint is off, you will need to scrub the ceiling (and walls to be painted) with a strong cleanser like Tri Sodium Phosphate or even a strong Tide solution, with two subsequent rinsings. Then when dry, sand with a random orbital sander using non-clogging paper, then wipe down with clear water twice. When completely dry, you will be ready to apply your paint. 4 years after applying mine, it looks like the day I applied it, and we don't use our fan very much in the face of daily hot showers.