25% every two weeks isn't enough water changes to keep your fish healthy. The ammonia built up in the water can lead to infections.. which is what pop-eye is. Keep his water scrupulously clean with 1 x 50% water change and 1 x 100% change per week to help prevent him getting worse/anything else.
You said you're re-cycling his tank? With the fish in or out? I keep small tanks, and I know very well that they are very hard to cycle (especially with no filter..) and keep stable. The only cycled one is a heavily planted 3.5 gallons, and I watch it daily like a hawk for any signs of imbalance.. The others are all changed to that schedule above, and that keeps the ammonia down.
So the water quality needs improving and to be kept steadily that way. If you follow the directions for treatment in the sticky and keep an eye on the water for ammonia and nitrite buildup, I'm sure he'll be better in no time.
Bettafix isn't an antibiotic, btw, it's an antiseptic that may not help an infection much once it's set in. There's some good antibiotics recommended in the sticky.