Is this limit cycle caused by the residual of the digital AI filtering at the half sampling freq and that his the threshold?
Or is this some nonlinear effect? If this is a linear effect associated with the zero-padding, the absolute
value of the DC may affect the amplitude of the oscillation. (Or equivalently the range of the DC where we get this oscillation.)

Anyway, it seems that we should use no-zero-padding.

You pointed out the ringdown of the digital AI filter in the sample-hold case (i.e. no-zero-padding case).
How does it look like in the conventional zero-padding case?