Originally Posted by DoubleNickel
Tried to iron a loose section back down (as a test); the adhesive doesn't appear to be heat sensitive...but the edgebanding certainly is....
I don't know how that edge banding was originally held in place, but most plastic edge banding is applied with heat. When the original glue fails, applying hot-melt glue to the either the banding or to the edge it is covering will often work. You apply the hot-melt glue, spread it, let it cool, and then iron the banding back in place. Make sure that the iron is not too hot. Excess hot-melt glue will squeeze out. Leave it there until it is cool and hard and then remove it with a file.
Obviously, getting the correct temperature of the iron is critical: melt the glue, but not the banding.