I just looked at your post a little closer and saw you made reference to the OUTPUT ASSIGN (SEPARATE) as per X1 and SD1/SD1Plus.
On the X and SD1 Series, you were able to go to OUTPUT ASSIGN and choose SEPARATE 1, 2, 3 4 [F5] which displayed a screen that had ALL arranger parts (Chord 1-5, Bass, Drum1, Drum2) and you could [for each one] assign to either output, correct?
On the AUDYA, this detail degree of assignment can't be achieved (as of OS 4.1 or earlier) ... the reason being that - in this system, the outputs are GROUPED such that each pair is routed to an effects bus, thus eliminating the loose of effects (as was experienced in the older SD1 and X series) when separate outputs are used simultaneously. This is why in the case of AUDYA, the outputs are GROUPED (1&2), (3&4), and Main (L&R) which 'limits' your capability to truely assign 'any' part to 'any' output, but rather you are compeled to use the parts displayed per output selected.
Hopefully this now better explains your delima with the output issues and I am sorry if I mis-understood your initial request ... a lot going on as you can see.
If your issue however is you have been able to get the outputs routed the way you like and you have followed the SAVE procedure (as outlined above by me and others) and somehow your machine is NOT saving your settings, you might need to have that unit checked (unless there is some other user setting/error I am not aware of at this time).