Are you doing frequent water changes keeping his water real clean? Their fins are fragile and ammonia build up (which you can't see) will deteriorate their fins. Nitrites in the water will encourage bacteria to grow which will eat your fish's fins. And some fish seem to have more delicate fins then others. Make sure you keep your betta tanks REAL clean all the time (no slacking ever, one day can make a huge difference). If the damaged fish, make sure he's in a solo tank, keep the water clean (like do 100% water changes ever day, even switch out the tank/container every day with a clean one), don't overfeed. You can use Melafix to keep the bacteria buildup down but keeping the water clean is most important. If the finrot continues, you may need to go to more drastic measures--using an antibiotic to kill off some of the bacteria (and continue with the water changes to keep the water clean). If the finrot get REAL bad, and this is for truly last-ditch, you can paint ONLY the fins with peroxide to kill the bacteria (your fish will hate it, it'll look extremely sick for awhile too so don't do it unless nothing else has worked). Also, try not to put your hands in your fish tank or touch your fish--your hands and fingernails carry a lot of bacteria you can't ever wash off (not to mention the stuff you can get room fish tanks).