For some instruments, the number of significant harmonics produced may change over different pitch ranges. The partials of the very lowest and highest notes for some instruments may exhibit some inharmonicity. The number of harmonics that can fit below the anti-alias filter cutoff below Fs/2 will certainly be lower for very high notes. Your HPS pitch estimator mdy want to take those factors into account.

The attack transient of some instruments may produce a spectral band of noise which may overlap with the HPS search region of some pitches or their significant harmonics.

Potentially, the overtones of very high frequencies might even wrap around Fs/2 if the low pass filter before the audio ADC doesn't have a good enough stop band attenuation.

For some instruments, the number of significant harmonics produced may change over different pitch ranges. The partials of the very lowest and highest notes for some physical instruments may exhibit greater inharmonicity. The number of harmonics that can fit below the anti-alias filter cutoff below Fs/2 will certainly be lower for very high notes. Your HPS pitch estimator mdy want to take those factors into account.

The attack transient of some instruments may produce an aharmonic spectral band of noise which may overlap with the HPS search region of some pitches or their significant harmonics.

Potentially, the overtones of very high frequencies might even wrap around Fs/2 if the low pass filter before the audio ADC doesn't have a good enough stop band attenuation.