> So what's going on there -- does the voltage vanish

yes. BBDs are an array of very small capacitors and FETs (used as switche
that pass on the the voltage of a stage to the following stage, a little bit
like a S&H, that's why it's calle "bucket brigade"). The capacitors are able
to hold the voltage only a limited time (I assume in the 100ms range but in
the data sheets of BBDs this parameter is not specified) and there is a loss
during each stage - same as for a real bucket brigade where some water drops
may be lost in each stage.

> or infinitely approach some value

as far as know the capacitors discharge to GND, but I'm not sure as it is
not specified in the data sheets. It may even depend upon the type of BBD.

> Can the coefficents be calculated and apply some kind of an
> amplifier and feedback to keep the data valid

No. You have no access to the internal stages of the BBD.

btw. The planned universal AD/DA module (the clocked delay) will be able to
delay control voltages too - clocked or (virtually) un-clocked with a clock
rate that is much higher than the CV changes.

Best wishes
Dieter Doepfer