The tape around the drywall ceilings in our house is coming down. How do I fix it?

The ceiling is textured, so I can't just put spackle on top because it wouldn't look right. I'm afraid if I try to glue it or put cauk under the edges, it will cause the drywall on the ceiling to flake off. The only thing I can think of is to put crown molding up against the ceiling to cover and hold it up. Any other ideas? Thanks for your help!!