What causes this high frequency "noise" in HHG spectra? Looking at high harmonic spectra, one can often see that peaks corresponding to higher harmonics look more and more noisy and seem to be drowned out by the noise.
For example, one such spectrum is Fig. 2 of this publication. The phenomenon can be clearly seen from the 9th to 19th harmonic and again in fig. 5 around the 17th and 19th harmonic.
Another example would be fig. 3 here or figure 3 in this paper.
 A: There isn't a single clear-cut answer, but rather a combination of things.


*

*Noise is always present, whether it be in experimental spectra or in numerical simulations. 
(All your examples are numerical simulations. While this does not invalidate your observation, there is some room from the claim of "I see this feature in all numerical simulations I've seen thus far" to "I see this feature in all HHG spectra".)

*The noise is very often at a constant-noise-floor level. (In numerical simulations, this often comes from the intrinsic limitations of apodizing the signal.) The HHG signal, in contrast, generally goes down with harmonic order, and at some point it gets drowned out by the noise.

*The examples you give are all from HHG in solids, which is much messier than HHG in gases and isn't completely understood at present. In gases, the relationship between the microscopic single-emitter spectra and the measured signal, mediated by the propagation in the medium, is well understood. In solids, the microscopic simulations have a shakier relationship to the measured signal, with things like dephasing and the role of propagation still to be fully understood. So take all numerical simulations of HHG in solids with at least a grain of salt.
