If it has the vinyl material with the orangish foam backing, the issue is that the vinyl separates from the backing and falls - it's probably not the strip. There are a few things you can do, but I'm actually working on removing ours - it's a LOT of work but looks really cool when it's done. There are a couple threads around on it.
Other solutions include trying to tack it back up, but I didn't have much luck with any solutions I tried, such as using small screws with those caps, because then it'd just be hanging down between the screws.
If it's a different ceiling material, then disregard this post entirely.
1995 Airstream Classic 30' Excella 1000
2014 Ram 2500 Crew Cab with Cummins 6.7L Diesel
Sold but not forgotten: 1991 Airstream B190
Sold: 2006 F-250 6.0L Powerstroke Supercab