The original saddle from my Miyata 100 was peeling away from the foam underneath. This can be fixed using lots of contact adhesive sprayed in the gap between the two layers:
After waiting a few minutes for the adhesive to become tacky, I could pull the top cover tightly over the foam and press it back into place. I then wrapped the saddle up with an inner tube overnight to make sure it was secure:
The repair came out well, and the top was no longer peeling away from the base:
