They'll get increasingly niche, but continue to exist as long as there's a market for them. That market will certainly shrink as broadband becomes more ubiquitous and affordable, but it will still be there for quite a long time to come.

There seems to be this common conception that if you're personally not using a technology, then no one must be using it. My mom was still using 3.5" floppies until a couple years ago, and I haven't even laid eyes on one in over a decade. They're still being sold at Office Depot. So obviously there's enough of a market left to justify manufacturing them.