Not gone, so much as badly in deed of fresh concepts and ideas. Like consoles, they need to make them into one stop, all around good entertainment devices.
For the vast, vast majority of people, they are "good enough" for their on the go gaming needs. People do not want to carry around two redundant devices, especially since the gaming handheld is the functionality loser of the pair.
Dedicated gaming handhelds are dead. There's a chart that somebody put up on GAF a while back tracking what happened to the sales of dedicated gaming handhelds when the iPhone launched. It didn't move the needle much, at first, but when prices of those phones fell in line with gaming handhelds? It was a very sharp decrease in sales.
The worst thing Nintendo or Sony could do is make another "me too" tablet or phone focused on games. Put your IP on the stuff that already sells or watch it depreciate into the toilet. Ain't no room for pride in business.