It's not predators so much as habitat. Kill all the fox and raccoons and what happens? Skunks and snakes just eat that many more eggs and chicks. Every predator out there will eat quail or their eggs. Get rid of one kind and another will take up the slack. You know what eats more snakes than any other predator? Red-tailed hawks. You know what like to kill fox? Coyotes. In decent habitat a quail hen can raise 2-3 broods per year. Most nests will fail or young die. If that happens, she'll likely renest. That's just how it is being at the bottom of the food chain. But if they have the proper nesting, brood, roosting and escape covers, quail will prosper. Hard winters or cold, wet springs can set them back a year or two; but they'll recover if the habitat is good, regardless of predators.
VictorCharlie hit it on the head when he brought up tall fescue. Worthless for quail and it's everywhere. And those brushy fence rows you remember from when you were a kid. If they're still around, they're old or mature timber now. Good for deer and turkey but of no use to quail. They like low, brushy cover. Stuff you hate to try and walk through, like blackberries, rose, or plum and dogwood thickets. An oak woodlot with a bit of sumac on the edge ain't gonna cut it.
Farming's changed. Around here it's mostly fescue pasture and hay, corn and beans. Not much small grains or lespedeza and with commercial fertilizers, there's no need to let fields idle for a year. A piece of ground left idle will come in with all manner of annual forbs that are ideal for quail. They provide seed and insects they need to eat. There's overhead, vegetative cover to offer protection, and bare ground between the plant stems for the young chicks to get around through. Chicks can't walk through fescue or other sod forming grasses. In addition, fescue doesn't have many insects, and chicks need the protein in insects to grow.
Oh yeah, kill all the cats too.