Well if you want to look at it from a WWE standpoint, it's because of their focuses. As someone pointed out, being called a suplex machine was good because the crowd were impressed by your in ring technical ability. The reason you don't hear it, or see it, nowadays is because the WWE no longer focuses on that. They focus on the entertainment aspect, and suplexes just aren't held in such high regard. If you think of Chris Benoit, he was renowned for his technical ability, but his mic work wasn't up to scratch. And by the end of his career, he was languishing in the mid card and on ECW.
You could also say that suplexes are simply too dangerous for WWE's liking, and you would be right. I'm not talking about vertical suplexes. I'm talking belly to belly and germans and the like, where head drops are common. And Vince just doesn't seem to want to risk his wrestler's safety on a regular basis.
But in general, the art of the suplex lives on. Especially in TNA where wrestlers like Kurt Angle, Samoa Joe, Desmond Wolfe and even Hernandez hold the mantle of suplex experts. Also, you cannot forget about ring of Honor.
It thrives in the land of puroresu, where suplexes are as common as clotheslines. In Japan, wrestling is shown as very like a sport, and they aim to do their best to hurt their opponents. I'm not talkning murder, but using hard kicks and lariats, and strong suplexes where you often get head drops. The brain buster, their equivalent of a vertical suplex, is seen as dangerous, and something you never see in WWE.
So as for the art of the suplex disappearing, yes, in the WWE. However, it lives on in different parts of the wrestling world, and is still going strong.