When moisture in the bathroom or kitchen causes the laminate facing to come off one of the cabinet doors, the first thing to check is the condition of the core. It's usually made of medium density fiberboard or particleboard, and if you see swelling or blackening from mold, you're better off replacing the doors than trying to re-glue the laminate. If the core is sound, however, re-gluing the laminate is a fairly simple procedure.
Procedure for Re-Gluing Laminate Facing
Although you don't have to remove the door to re-glue the laminate, the repair is more likely to succeed if you do, because you'll be able to clamp the door to secure the glue bond.
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Unscrew the hinges from the cabinet with a screwdriver. Remove the door, and then unscrew the hinges and put them aside. To to make sure it doesn't get in the way, remove the handle also.
Lay the door flat and peel back the laminate with your fingers as far as it will go. If the doors have laminate edges that have come loose, peel those back first, and then peel back the facing. Don't disturb any glue bonds that you can't separate with reasonable force.
Apply solvent-based, waterproof contact cement to the exposed core as well as the underside of the laminate surface that you peeled away, using a small paintbrush. Don't overdo it -- you just need a thin layer of the contact cement on both surfaces.
Keep the surfaces separated by putting a pencil or a ruler between them, and let the glue set for about 10 minutes.
Remove the item you used to separate the surfaces, and press the laminate onto the core. Put a piece of scrap wood over the glued area on the front side of the door and another on the back, and then clamp the two pieces of wood together with a C-clamp to apply more force and secure the glue bond. You don't have to keep the surfaces clamped for long -- five minutes should do it.
Release the clamp, and glue any more laminate that has separated in the same way. Finish up by re-gluing any edging that has lifted.