The University of Georgia did a study and came to the conclusion that the Southern accent is fading. Less formally, a word game website did a survey that found the standard New York accent is fadingas well.

The Georgia study largely attributed it to migration and people moving more than they used to, with a focus on growing metro areas in the south. Though apparently some younger generations are trying to shed their accents to sound more professional, and the internet is creating a sort of average American accent.

Though nobody is worried they'll disappear entirely at the moment that I can find.