I have seen that all too many times from neons and cardinal tetras. Once it reaches that point they will usually be dead within a day. That is the problem with neon and cardinal tetras. They're very sensitive and are prone to disease.
Best advice I can give is next time purchase from a different supplier, make sure they have had their stock at least a week. I would find out what day they get their shipments in, and go buy your fish from their EXISTING stock the morning of, or night before the new group arrives. That way you can at least know the store has experienced the initial die off and the remaining fish are healthier.
Other points you must consider is that neons love soft acidic water. It isnt TOTALLY necessary, but will help. What IS totally necessary is that your tank is mature, and has zero traces of ammonia or nitrite. If your tank isn't cycled fully, it is a death sentence for just about any fish.