There is a rod, but for whatever reason, it doesn't go quite go the full length of the heel. I have had this exact failure once before, cf. p. 80 of this thread. Those shoes were also Nine West, different model, but of the same vintage. Oddly enough, I bought both of them brand new and owned them for more than a decade before failure. I can't actually see it on these Planteras, but I guarantee you that the heel is beginning to break right where that metal rod ends. Why they didn't make it a little longer to go the full length is beyond me, but I only know that it is so.
If I decide to attempt some kind of repair, I think I'm going to go with the superglue, simply because it takes quite a bit of force to get that crack to open up enough to get something in there, so I'm hoping the crack is less than halfway through the thickness of the heel. I don't want to break it more trying to get something more viscous than superglue in there.
I have no scientific evidence to back this hypothesis up, but it is my guess that the failure has less to do with the inadequate stiffening of the heel, and more to do with the aging of plastic. Unless something goes terribly wrong, I think I have at least another decade or more of wearing heels left in me, so I shall be interested to see just how well some of these plastics hold up longer term, and what causes them to fail.