Welcome to the Mitchell & Johnson thread
@Sujay Rao . Glad to have you here. Interesting post. Sorry you are having problems.
I don't have an Onkyo dap to try reproducing your results. Have 2 PonoPlayers. They use two 3.5mm trs for balanced (same as original Sony balanced). Twin 3.5mm trs or one 2.5mm trrs will support balanced playback. A "quirk" of the Pono/Sony balanced system is that with headphones with 3.5mm trs in each cup, standard 3.5mm trs to 3.5mm cables won't work! The Sony/Pono end uses tip for + and ring for -. So custom cables must be wired up.
Some thoughts on your problem.
1. Have you marked the left and right cables at the ear cups correctly?
If plugged in reversed nothing will play. My balanced cable has left and right marked on the ear cup ends. I also have the PonoPlayer ends marked Left & Right. Even running my cable the wrong direction would result in the wrong connections (your setup won't do this).
2. The PonoPlayer has protection circuitry for balanced mode. If I pull the balanced cable out while on, it instantly senses it and defaults to single ended. Onkyo probably does something similar to protect the outputs. Is it possible that sometimes it thinks the connection isn't balanced and it mutes the outputs to protect them?
3. Don't know if connecting the cable's tip & ring together at the ear cup would enable the "auto channel" feature to function again in balanced mode. To me it is easier to mark the cables correctly and plug into the correct ear cup.
As I composed this message, I switched from balanced to single ended and back many times. No problems. They always played. This pretty much rules out a common ground existing between the ear cups. That would instantly knock the PonoPlayer into protection mode.
Hope this helps. Been a year since I listened to the MJ2 and Pono in single ended mode. Not a huge fan of the Pono in single ended or the MJ2 cable.