I think the likely issue is lack of hardness in the water, that is, lack of calcium in the water column combined with acidic pH. Have you tested your GH ?
Nerites come from tidal flats, where they are regularly exposed to full marine water conditions, which are very hard and alkaline. They do best in hard, alkaline water. If there isn't enough dietary calcium, they're that much more vulnerable to acid erosion.
You might want to try mixing tap water with some RO/DI from the store, but only to the point where it's still at least pH 7 or higher, and add calcium blocks to the tank for the snails to munch. I find the ones they sell with spirulina in them, vacation feeder blocks, work well for me, but my pH is not acidic, so in your water as it is now, they may dissolve too quickly to be helpful.
Fish can adapt to wide ranges of pH and hardness, what they need most is stability. If you choose to change the tank parameters to favour the snails a bit more, make the changes gradual, so as not to shock everybody with sudden change.
You might also try making snail O..a snail diet bound with agar or gelatine. Add plenty of calcium to it, and some spirulina, as Nerites can use algae. They'l eat some veggies but not many have enough calcium in them to help much. Recipes have been posted here and online.. a search should find you several to try.
If you continue to keep them in this water, the deterioration will probably continue to the point the snails die.
Edit.. I realize you have tetras which prefer a slightly acidic pH, but they are kept in a wide range of water conditions, as I said, stability is most important to them. If you can keep the tank pH just at 7 or very slightly over that, and be sure of a GH of 4 or more, the snails should do better and the fish should be just fine. I keep Danios & Beckford's pencilfish as well as a variety of cories, kuhli loaches, CPDs, Chili rasbora, cherry barbs, cherry shrimp, bamboo shrimp, ghost and vampire shrimp, all at a pH of around 7.4 and quite hard, which is the tap water this area has. All happy and healthy.