why does digital volume control cause loss in info

It doesn't. Digital volume control is commonly implemented using a module that is essentially a digitally controlled stepped attenuator. The signal is analog. The notion of "dropping bits" is pure myth.

There is a common digital volume control chip, used in my McCormack MAP1 six channel preamp, which does 1/2 dB steps. It is a stepped attenuator, and no motor is involved. If such a chip follows the D/A conversion no bits are lost. If an analog output is being produced there is no reason to use another implementation.

Now, if you want to have a digital output and attenuate the signal there will be a loss of resolution. No matter how you process the data a 12 bit output obviously has less resolution than a 16 bit output.

Almarg...I know about this chip because one failed in my MAP1 and was replaced (on waranty). Sorry I can't cite the exact part number. There are three of these 2-channel chips in the six channel preamp, so they can't cost that much.