The same thing happens in my car and seems to be a function of the output volume. If the volume is turned down too low the “No Aux” message appears until I turn it up, and it also happens on SOME audiobooks between chapters depending on the gap.
If I turn the volume on my player up all the way, it usually generates enough low-level noise to avoid the drop-out problem except for the longest gaps between chapters. In my case it’s more an issue with the car stereo than the player apparently.