I'm sorry you're having troubles
In an aquarium that size you need to be doing at least one 50% water change and a 100% water change per week; one water change alone won't keep the toxins at a safe level (fish poop and uneaten food release a toxin known as ammonia, and fish release ammonia from their gills instead of urinating). It sounds like he may have fin rot, which is usually attributed to poor water quality.
With clean water you should find that his fins start to grow back. You may want to do, for now, two 50% water changes a week and one 100% water change (remember to acclimatize your fish back into his aquarium when doing a 100% water change; also remember to rinse the aquarium thoroughly to remove any fish waste/build up of toxins/bacteria).
If you have any questions or concerns please let us know, there are multitudes of topics available that can explain the vast majority of things about betta care!