I had huge problems with the dual BNC connection between BluMK2 and Dave, with regular dropouts using BNC 3+4, and using BNC 1+2 I couldn't even get the Dave to recognise a dual BNC connection. My Dave was an early model with the domed glass display. I contacted Chord and was told I'd have to return it for repair (fortunately under warranty)... they changed the entire motherboard (and replaced the display with a flat glass screen), since then it has operated problem free using either combinations of dual BNC inputs.
However, even when I had these initial connection problems, playing CDs was never an issue, because the signal from the BLU when playing CDs (I believe) does not require both BNC connections (dropouts generally occur when Dave can't synchronise the two separate signal inputs), only one. Since you have the same issue with both streaming and playing CD's, it's not the same issue I have suffered... it sounds like there may be a problem with the Blu, or the BNC cables perhaps?