The question is why the PLA is taking their sweet time to make the decision. If you look at the J-20, the PLA didn't even hesitate. In fact, most of their high profile projects are going smoothly, from small UAV's to big Shenzhou launchers to gigantic 001A. Yet, the J-31 came out not too long after the J-20 but is still in the limbo.
The key difference between the two programs, and one crucially relevant to our discussion at hand, is that the J-20 program was borne out of a PLAAF requirement (i.e. a military-sanctioned tender) while the FC-31 is an independent project by SAC. The J-20 program would have had access to PLAAF funding, among other luxuries, that the FC-31 program would not. The same principle could be applied to other big-ticket items, such as the 001A or Divine Eagle UAV.
Except for the rumored second unit, which we have yet to see, there is virtually no movement whatsoever. Every once in a while, we get a few photos of the J-31 taxing or flying. There has been no change done to the unit whatsoever. In comparison, we see tons of changes to the J-20 whenever we get a new model. We know they are working on it. Is it possible that the J-31 is so perfect when it first came out that nothing can be done to make it better? Hardly. A likely situation: it is now so low on the priority list that no one bothers to even work on it.
Lack of publicity does not necessarily imply that there is a lack of progress. Granted, the FC-31 seems to be on the backburner until the PLA makes its decision, but keep in mind that it has been increasingly difficult to gauge the progress of Chinese military projects in recent times. The J-11D, for instance, remained unknown to the public until it conducted its maiden flight. Same thing could be said for the Divine Eagle UAV, Sharp Sword, and a host of other platforms.
That being said, there are numerous rumors, as well as official statements from SAC itself, that an improved functioning prototype is being pursued.
It shouldn't be about the funding. With so many high profile projects going at the same time, it's hard to believe that adding one more would become so big of a burden that they have to slow it down.
Funding, au contraire, is a huge factor in the success of a military project. The FC-31 used funds directly from SAC itself rather than China's DoD, so it is definitely a burden for SAC. The YF-23, which supposedly out-performed the F-22 in kinematics, was canceled precisely due to lack of funds.
One likely explanation is that the PLA simply doesn't like it. It still exists because the PLA is being polite and doesn't want to say it out loud.
We cannot make that assertion solely based on a lack of progress. It would be unwise for a company to continue development of a project that its customers remain undecided upon, but that stagnation alone is not indicative of the customer's intentions.
Is it possible that SAC might eventually find some genius who might be able save it? It could happen... But the chance of that happening is slim. A genius might want to have a clean slate and design a new system instead of making changes to a failing system.
Frankly, my guess is that the J-31 still exists because some big head honcho at the SAC is using his significant political influence to keep it alive...
Two things stood out in your post: (1) why are you assuming that the FC-31 needs "saving", and (2) how did you arrive at the conclusion that it is a "failing system"?
At this point, we simply do not know what the PLAAF/PLANAF's feelings are regarding the FC-31, nor do we know its capabilities well enough to form our own assessment of its prospects. A lack of publicity regarding the FC-31's testing regime is by no means implicit of its rejection by the Chinese armed forces. Additionally, rumors claim that the PLAAF's decision will not come until late 2016.
