I have had to re-glue almost every burl door facing in my coach. As I understand it, they tried a new spray adhesive on the veneer in some coaches and it does not hold. To do a repair you will need a deep reach clamp that will reach the area you are going to re-glue.
You can buy these at Harbor Freight or some other tool outlet that sells cheap tools. Use a white glue like Titebond II. Do not use Gorilla Glue as it will expand and come out of the joint and be difficult to clean. Work a little glue under the area of the veneer that is lifting, with your finger or a business card. I then use my finger to press the veneer to remove all of the excess glue. You can wipe the area with a damp paper towel before your clamp. Use a block of wood on both sides of the door so as not to damage the finish when you clamp, 3/8 inch plywood works well for this. I use a paper towel under each block as padding. The paper towel will also prevent the glue from sticking to the block if some extra comes out. Remove the clamps after about an hour and use your finger nail to clean off any extra glue. I have re-glued most of the edges of the door veneer in my coach using this technique. Once the edges are down the center should not ever lift.
Good luck
Tim