What is the time limit for keeping 'fertile eggs' before they need to be put in to hatch?
How are you storing them? That has an effect.
There is no set time where the switch flips and every egg goes immediately from hatchable to unhatchable. Each egg is different. Some factors to consider are storage temperature, humidity, and turning.
This is the internet, you can read many different "ideal" storage temperatures. I've settled on 55 F (13 C) as a pretty good temperature to shoot for. The further you get from that ideal temperature the faster they deteriorate. The longer they are at an extreme temperature the worse the effect. If the egg actually freezes the cells rupture so that can be pretty fatal. Near freezing is not necessarily a death sentence but I would not want the egg at that temperature for very long. Above a certain temperature the egg starts to develop but it is not warm enough to sustain development so the embryo dies. I store my eggs in the house so temperatures are in the upper 70's F in summer and I get decent hatches. I'd be concerned if the temperatures got in the 80's F (above 27 C) for very long.
The eggs lose moisture during storage. If they are stored in high humidity they lose moisture a lot more slowly than if stored in low humidity. Basically the higher the humidity the better as long as you do not get condensation on the eggs, which could affect the bloom.
Turning before incubation serves different functions. It stops the yolk from settling to the bottom and touching the inside of the shell where it could get stuck. It also helps mix some of the fluids in the egg. Some people think not turning during storage is a death sentence. It is not, you can still get decent hatch rates even if you don't turn them, but turning them during storage improves hatch rate. I think it is important.
The experts, the people that do this for a living, say that you can get good hatch rates with two weeks storage if you maintain ideal storage conditions. They generally work with the hatcheries to see that ideal conditions are maintained. They know what they are talking about.
In real life there will be exceptions to this. You can find stories where eggs were stored longer than 2 weeks and in less than ideal conditions and still hatch. But the experts would not depend on that.
I do not store my eggs in ideal conditions. I store them where it is too warm. Humidity in the house is often fairly low due to air conditioning. I turn them 3 times daily. I do not store them longer than one week and usually get good hatch rates. Not usually perfect but decent. I don't know what would happen if I let them set several more days, I've never tried that.
Good luck!