The smartphone industry has a culprit to blame for slumping sales: Its old devices remain too popular.

Flashy phones of yesteryear, particularly Apple Inc.’s iPhones and Samsung Electronics Co.’s Galaxy S handsets, are getting refurbished, and U.S. consumers are snapping them up. Many shoppers are balking at price tags for new phones pushing $1,000, and improvements on latest launches in many cases haven’t impressed.

As...