Bookbinders are magicians. If the glued pages are simply falling out then there's no damage to the binding edge, so they should be able to fix it.

The only thing to worry about is that TMA was printed with the binding in mind, photos printed edge to edge across pages for example, with very tight inner margins in the gazetteer.

If you had a traditional stitched bind done, you may have trouble reading and seeing the print near the spine, so it would probably have to be re-glued.

AMD