The obstacle is that after evaluation, neither the PLAAF nor the PLAN deemed J-31's performance satisfactory to merit public investment with government funds. We don't know why; if it is a fixable flaw, it may be corrected on future prototypes to redeem the aircraft for China's armed forces but if it is a problem with base design that incremental improvements cannot address (satisfactorily), then we will never see this bird enter service.
Quite frankly, my enthusiasm for J-31 is low. If the Chinese military has dragged it's feet on this design so badly, then I'm afraid that even if it eventually becomes accepted, it's still only borderline satisfactory. I don't drag my feet on things that are fantastic; I do it when I've got no other choice so I have to settle.