Neons are hardy in my experience, but, are very susceptible to nitrogenous waste. They should never go in an UNcycled tank, or one with OTS. However, in clean tanks they are very hardy can live for more than 10 years.
On a side note, of the 12 that died listed above I never found a trace of one- EVER. Don't freshwater fish usually float when they're dead?
The tetras that I've owned have always fallen to the gravel. If they fall, then the fish may start pecking at them. Whether the fish ate the dead tetra or not, we may not know. I have yet to see a floating tetra when it dies, even at the pet stores.
sounds like a typical fist store. neons are known to die off.
how long has the tank been set up?
whats in the tank?
have you tested the water? ammonia nitrates and nitrites
you might need to read up on cycling.
http://www.aquariacentral.com/forums/showthread.php?t=84598
i wouldnt trust anyone at the LFS.