After I increase the rate of the whole song, increasing by 50% (1.5), there is an attenuation of about 6 db. This seems to be the same at a new rate of 1.75. This doesn't seem to occur when slowing...

This is the nature of the music, I think, not an algorithmic problem. Increasing the rate with time stretching means the lower frequencies get less and less periods, and lower freqs make most of the amplitude.