Hi Amit,
Is your issue solved?
I hope you have all the three methods of order_save Badi
CHANGE_BEFORE_UPDATE
PREPARE
CHECK_BEFORE_SAVE
If still it is not getting triggered. Can you check when you only edit payment data assignment block, do your functional spec have any specific pre- requisite. If yes, check if you can use PPF action methods.
I tried editing Billing Assignment block on Service contract and saved. Order_save badi gets triggered for me. Is that your custom button??