That's what I did when the headliner started to fall in my AMX (after 25 years). The shop re-glued it, and it held for about 24 hours. Fortunately, I found a "fiberglass" reproduction headliner, and I had that installed and there was no more problems.
Since adhesive technology seems to be going backwards, (at least in Germany) maybe some interprising individual will eventually make a fiberglass mold of the current Crossfire headliner (from a salvage vehicle perhaps) and reproduce it for the rest of us. Because it looks as thought we will "all" eventually need it.

Or the Crossfire Forums resident "Barrister" (that we have on retainer) could add that to his list of "Class action law suits" that he plans on filing against Chrysler on our behalf. For:
1. Door Rust
2. SRT6 Rear Wing "bracket" rust
3. Bucket Seat "Heating Elements"
4. Roadster's rear Window coming loose
5. Coupe's Headliner falling