should i try artifficial inseminations?
I wouldn't, personally, AI in even large birds often results in damage and necrosis, I wouldn't like to risk it in such a small bird, and really quail aren't normally known for being hard to breed...
Is the male actually mating with her? Reproduction can go wrong at any point and I've had my fair share of males that would mount but not mate. Sometimes the hen would crouch but then just not get into position in terms of turning her tail and moving it out of the way, so no matter what he does it isn't going to happen. Observing the interactions between the male and female can pinpoint some issues.
Have you wormed them recently? Some worming treatments, and other parasite killers, can cause fertility issues within the next few months to a year; some brands state not to breed them for at least three months after using their product. Anecdotally many people have long term issues after wormings, it pays to remember animals have different sensitivities just like people do, some animals don't take well to some wormers.
It's odd that she gives up brooding after a few days. That could prevent you seeing any evidence of fertility all by itself. Is she too young? Really if she's brooding at all she should be old enough and should continue to brood...
Is something disturbing her? Maybe you are, accidentally, some hens cannot stand being checked in on, or maybe it's the male? Some males lack sufficient instinct to leave brooding females be, and will even mount them on the nest, which can be very damaging for both hen and clutch. Is there something environmental that's disturbing her maybe? If she feels the nest isn't safe, many hens will just abandon it. Is it overly exposed maybe?
Bacterial infection can be another thing that causes her to abandon. Sometimes there's a resident or transient bacteria that either resides in a place or passes through and it can destroy developing embryos, and very quickly they can start to decay, even before showing development this can happen; when this happens the egg begins to resist warming up, cools down abnormally quickly, has a different sound when tapped against the other eggs, and feels different under the hen.
Smart ones will then reject that egg, but some will just leave the whole clutch. Some very aggressive bacteria transmit via the skin, feathers, nesting material, and contact with other eggs, and can kill even hatching eggs within a matter of hours, by inducing something like toxic shock. Your hen may have some bacteria on the feathers that is killing every clutch and causing her to abandon early.
If she's just not working out as a broody/mother I'd put her on the backburner so to speak (figuratively if you only want her for eggs, literally if you want her to brood and mother and continue a line with solid and reliable maternal instincts). I'd consider getting another quail hen, maybe a couple, maybe even another breeding pair. I've not done artificial incubation so can't help out with that, sorry.
Best wishes.
