Hi Woody,
If you are confident with a steady hand and good lighting, you can easily do this with superglue ...
very little is all you need. And have a small paper towel dampened with solvent ready (like Goof Off or the like) if you apply too much superglue and it oozes out (which is why you use
very little to avoid this). You want to avoid not only the mess and clean up, but you also can glue your finger to the binding ...not exactly what we mean by being attached to our favorite instruments
All very easy to do. But if you're not confident with it, then any good/trusted guitar tech can do this as it's pretty standard stuff that happens to any guitar with biding a some mileage on it (be sure he is, indeed a trustworthy guy, of course).
And as SF so aptly advised, check your room's relative humidity. You
do have a hygrometer in the room where your guitars are sitting, right?? (ahem, right?!!!
).
Edward