the problem when they go saggy is that the thin layer of foam between the vinyl and the actual headlining degrades over time and thats why they go saggy. if you glue it up again you're glueing to the crappy foam again so ideally you need to strip the foam off and glue to a good surface. obviously this is a lot of work and you can cause more damage doing so.
you want a high temperature resistant impact adhesive.