OK... so there's not enough material to just tuck it back in?

It's hard to say, exactly, from here, Zsa Zsa Gabor It kinda sounds like the vinyl has shrunk, which is an odd one. There's usually plenty of vinyl there to stay tucked in. I'd probably just remove the piece and check it out. If you have what I think you have, it only takes a couple minutes. Find all the screw heads, carefully untuck the vinyl to expose the heads, and unscrew. It'll make more sense once you have the piece off/out - you may have to reposition the vinyl to allow enough room to tuck - or possibly glue that section and forego the screw there.

It sorta looks like the ceiling panel is pushed up slightly - possibly that allowed the vinyl to come untucked?

 

Dennis, the vinyl untucked, I tried to glue it but there's a foam backing and the glue didn't stick. If I untuck the cover, get to the screw head, then I'm right back where I am now.

What am I missing?

 

Is the entire trim piece pulling away or just the vinyl? If just the vinyl, tuck it back in. If it's the whole piece, then most likely... find that screw head by feeling through the vinyl. Then gently pull the vinyl out (from being tucked in) to expose the head. Do the same for any others that you need to.