.
I am all out of ideas.

It is my experience that it is default Knoppix LiveUSB-with-persistence behaviour that volume control setting changes, by either of the guis that arise from either right-click or left-click of the panel speaker icon, are retained via persistence on reboot.

lspci | grep audio indicates my audio device is an
Intel Corporation 82801I (ICH9 Family) HD Audio Controller (rev 03).

If you were to make an new KNOPPIX LiveUSB with persistence, made no change in its initial configuration, and if your audio device is like mine, I can see no reason your LiveUSB would act differently than mine.

If your hardware or software configuration differs from mine, then obviously some configuration difference may explain a performance difference. ANY difference in configuration may explain different performance. You are in the best position to know what differences there might be in your configuration and a default Knoppix configuration.