Harmonic Product Spectrum limitations in pitch detection
It could be that too few harmonic partials are present in the signal at these higher pitches. The HPS algorithm is pretty simple and relies on those upper harmonics to keep stacking up until the fundamental emerges from the background. Of course, we should wonder, what's your sampling rate? If it's 8000 hz, then there's only room for 3 harmonics of a 1000 hz pitch...