This has nothing to do with AC voltage, but rather any kind of voltage bias. There is a similar (but typically even more pronounced) loss of capacitance seen under DC bias.
There is a property of certain dielectrics that is very similar to ferromagnetism (what makes things like iron magnetic) called ferroelectricity.
Just like how ferromagnetic materials will, in the presence of an external magnetic field, have magnetic grains align, resulting in an additional magnetic field produced by the material, a ferroelectric material will have dipoles align producing an electric field if suitably excited by an external electric field.
Essentially, certain types of ceramic act as something analogous to a magnetic core in an inductor, but as an 'electric core' in a capacitor. The dielectric serves to massively increase the energy stored in an electric field, increasing the capacitance just like a magnetic core does the same for inductance.
And just like magnetic cores, these ferroelectric dielectrics can become saturated.
With an inductor, as current increases, the effective inductance begins to fall, as the magnetic core can't store any additional energy/strengthen the magnetic field further.
The same is true with ferroelectric materials. Voltage, rather than current, is the determining factor here, as voltage determines the electric field (where current determines the magnetic field). As the voltage increases, the capacitance falls as the dielectric is increasingly unable to further strengthen the electric field in the capacitor.
A common mistake I see made is the assumption that the voltage rating of ceramic capacitors has anything to do with this. It does not. Picking a ceramic capacitor rated for a higher voltage will generally have almost no impact on the amount of capacitance lost vs. voltage bias (AC or DC). The only thing that really matters is the physical size of the capacitor. Bigger ceramic capacitors will have more dielectric material, and more material means it will lose less capacitance as the electric field through it strengthens. Just like physical size does the same in the magnetic cores of inductors.
C0G capacitors do not have this problem at all, as they do not have ferroelectric dielectrics. But nearly all high capacitance value ceramic capacitors do use ferroelectric dielectrics, and will lose (unfortunately, often a lot) of their capacitance under even a few volts of AC or DC bias. The only way to mitigate this is to use larger (and pricier) ceramic capacitors, or simply more of them. At the end of the day, if you want that capacitance, you need more volume of dielectric material, at least if you are relying on ferroelectric dielectrics to do it.