Electronic – Why crystal capacitors have to be close to each other

My guess is that the inductor is probably not a major contributing factor to the failures. I say this because it's a inductor, and as such produces a magnetic field. The quartz in the crystal is not particularly magnetic. Second, you note that the inductor is shielded, so the external leakage field should be small. Still, the crystal output is pretty high impedance and induction could be adding a small voltage in series with it. This should be small and not much issue if the crystal is being driven properly with the right load caps.

I would look closely at the crystal circuit. This sounds like maybe you are using too low of a drive level setting or the load caps aren't right. What does the datasheet say the load capacitance of the crystal needs to be? What size cap do you have on each side? The chip driving the crystal may have different drive level settings if it's intended to run with a wide range of crystals. At 24 MHz you almost certainly should be using the highest drive level choice.

Look at the crystal driver output pin (input to crystal) with a high impedance probe. That should be a good strong signal. It could be sortof square wave looking with a bit rounded corners or nearly a sine wave. It should be a few Volts p-p, usually half the supply voltage or more. Check the frequency carefully to make sure it's not running on a harmonic. If it is, it's a indication one or both load caps aren't connected or are too low. Then look at the crystal output. That should be a nice 24 MHz sine wave at least a Volt p-p, preferably a little more. Does the unit suddenly work right when you put the scope probe on a crystal lead? If so, it's again missing, bad, or incorrect load caps.

7 mm between a 25 MHz crystal and the chip driving it is no big deal. What is far more important is that the ground side of the crystal caps connect back to a ground pin on the part, not just punched thru to the ground plane. You don't want those high frequency currents running accross the ground plane else it will become a center-fed patch antenna. All the ground pins and other immediate ground connections to the chip (like the crystal caps) should be connected in a net with lines as short as you can manage, then that net connected to the main ground in one place only. This keeps all the little high frequency currents local, with only the external currents flowing accross the ground plane.