if the quail were in there for 2 days without food or water they diedof hunger. They require food and water 12 hours after hatching. They are much smaller with much higher metabolisms than chickens.
If you are talking about the quail eggs dying after two days, then most likely they were infertile. Quail lose fertility GREATLY after the first year of age, and have almost zero by age 3.5
Other possible causes are fumes from cleaning chemicals that didnt get rinsed out 100% during cleaning of incubator.
packaging distress/shipping distress/scrambling
not enough air circulation around the eggs...quail do NOT do well in the egg carton method of incubating.
If they were ferttile and stopped developing, it was probably your humidity.
They need 45%-55% until hatching, then 65%-75%. And you cannot open thi lid AT ALL since they are WAAAAY more suceptible to chilling than other species. Other than that, they are the same as chickens .
SO, have a brooder at 99 degrees ready and waiting with game bird crumble and electrolyte (or yogurt mixed with water) water. They need to go to the brooder within 12 hours of hatching, even if not all the way dry, and make very very certain to keep them warm and draft free. They seem to do best in a forced-air unit (fan and lots of warm air movement). "sticky" chicks often dry best after put in the brooder, they cure theselves very quickly with the extra air even if the humidity is the same as in the incubator. Just make sure they are very capable walkers/jumpers before you move them, and they will be fine.
I hope you decide to try again! Quail are so lively and lovely!