I agree, consecutive bouts with any malady should not occur. Healthy conditions appear to me a little off in the tank, which could come from not enough nutrient export (water changes, skimmer, carbon, etc.) and a buildup of nutrients in the tank.
If you have a test kit, please provide your ammonia, nitrite, nitra
te, and PH
readings. Also, please provide your means for filtering the tank..and any maintenance you do. Maybe we can find something simple for you to change and be very successful.
Once everything is straightened out, I would suggest making the 20g a nice home just for the clown and a new mate. The regal tang is just too big a fish in the long run that will grow fairly quickly and require a much larger (even larger than 65g) for the long run in no time. A better choice that will be easier on the bioload would be one or a pair of shrimp (my favorite are skunk cleaner shrimp).
Little tanks can be tough, but also really rewarding if you approach their strengths.