Not dead for sure, but they're not as predominantly the most popular ones anymore. Gone are the fifth and sixth gens, and the turn based RPGs suffered from that.
Although I do prefer turn based combat, its kinda hard to sit down and wait, sometimes the games or combat become tedious do that nature.
I'll always praise Tri-Ace for Star Ocean The Last Hope though, that's probably the most dynamic and fluent combat system I've played in a JRPG. True bliss.