One word: Gibson.
For much of the 80s, Steinberger was doing bang-up business and attracting a lot of star power. They were one of the leading guitar innovators of the 80s, without any question. Then Gibson bought Steinberger in 1987. For whatever reason, Gibson licensed the Steinberger patents out to makers like Cort and Hohner, who then produced cheaper, non-composite versions of the Steinberger in large quantities. Almost from that point on, the image of Steinberger was not of high-quality composite guitars, but of the licensed budget lines which (I think) eroded the cachet of the brand.
Steinberger was making Gibsons look old and stodgy in the 80s, and you know any kid who had enough money for a Les Paul Standard back then would have also been looking at the Steinbergers. The Steinberger looked like the future of guitar designs. Gibsons looked like the past.
I think for Gibson, it was a classic case of "if you can't beat 'em, acquire 'em."
Mmm. Looks like they killed a high quality American product...BA dum pshht.