Hi there

Well I'll just ask because if I don't someone else will - what are you nitrates? Shouldn't be an issue if you do regular water changes, but can't hurt to ask. Also, welcome to the forums!
 
Sounds like really poorly/weak neons to me - even if you're buying from several shops, depending the type of place you are living it could be they have the same supplier.Try cardinals; perhaps your local stockists have a better pool of these. They have a reputation for being hardier in aquariums than neons.

Oh and welcome to AC :)
 
I think you have the typical problem of poor quality stock. I would recommend not acclimating them to the tank, but QTing them until you know they are healthy. One of these times, you will not only get weak ones, but ones that have other disease that will affect all your fish.
 
Whats your water temp and have you ever tested your water compared to your fish stores? Could be a TDS issue. Lack of water changes, and only topping off can build your TDS levels very high which can hurt your fish even more than pH differences. Neons are pretty fragile. You could go with penguin tetras, cardinal tetras or brilliant rasboras which are equally stunning yet hardier JMO.
 
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