The only way I can see Sony even remotely considering a Vita successor is if it's pretty much a PS4 themed Nintendo Switch.
Where it can play PlayStation 4 games at a lesser resolution/framerate, most likely through downloadable titles, and all your Vita games through cartridges.
So pretty much a PlayStation Vita that can play digitally downloaded PS4 games, I would be interested in that tbh.
That's the only way I can see another PS handheld not failing like the Vita, and give it an advantage over the Nintendo Switch.
If it's in the same vein as the Vita though where it gets it's own library of games the PS4 won't get, and it's largely isolated, and can only play Vita games, PSP games, etc then It's not going to do so well.
It should also use MicroSD Cards, it was a very bad idea to use proprietary memory cards, and a program to be able to transfer music onto your system. It should be as simple as take memory card out, put it in your computer, upload music onto SD Card, put it in your handheld and play it.
Hopefully after the Vita's failure Sony realizes that inconveniencing customers for the sake of piracy protection isn't a good move.