Be advised that quail are the most creative creatures on Earth when it comes to finding ways to die.
So many reasons that this could have happened. Quail sleep as if dead, and their brood-mates aren't delicate about getting from Point-A to Point-B. If their buddy bird is sawing logs and won't move... right over the top they go. This could cause internal damage. A chick could drink funny and have the water go down the wrong way, and aspirate (drown). Drowning like this can be quick, or long and drawn out. The chick could have been born with a congenital defect or nutritionally deficient due to the health of the parents. The list goes on and on, as I said... it's not uncommon for quail chicks to be fine and then drop dead... cause unknown unless you wish to have a lab do a necropsy.
That said, check your heat source for teflon (coated) anything; even a teflon coated (some red) bulb in a light socket is toxic to birds. Confirm that there isn't cedar in their bedding. Examine whatever bedding you're using for moisture, as that could breed mold; the chicks breathe in the spores and blammo, sick or dead chicks. Put marbles or stones in the bottom of their shallow waterer to give them some traction to climb out of the waterer when they get into it... Trust me, they WILL get into the water. Double check the protein levels on your feed, chicken feed is NOT the same as gamebird feed nutritionally. Grind or crush the gamebird feed a bit more before serving to chicks as it's not quite as fine as they need it to be; they have tiny mouths.
Long story short, don't beat yourself up over the loss of the chick, with quail it happens. It's likely that there was absolutely nothing you could have done differently to prevent it.
