Have you tried using a slightly lower dosage? 0.5 teaspoons Epsom salt per gallon is OK.... but you'll want to use the lowest dosage that's effective for him.
In other words, if you can get the same results using 0.25 tsp/gal, or 0.33 tsp/gal, then that would be preferable to using the higher dosage.
But if you've tried this already, and he really needs the 0.5 tsp/gal, then continue to use this dosage.
What do you feed him? Foods that contain a lot of grains/fillers can be constipating. For example, foods that have a lot of corn, wheat, soybean, rice, gluten, etc can cause constipation issues. On this forum, the two most often recommended foods are New Life Spectrum Betta pellets and Omega One Betta Buffet pellets. Both contain a lot of proteins, and are less likely to cause constipation.
Also, if you can get live foods, especially mosquito larvae, this may help a lot. And a lot of people have had success feeding frozen daphnia.