I did hear a suggestion of PVA glue used with a syringe and needle, through the cloth. I've never tried it myself as I'm a bit scared of ruining the cards. You may be able to sponge off any excess as it is water based????? I may have to give it a go as the front two cards on mine have started to "droop" as you say! Powdered Viagara maybe!!!!
You could take the cards off and remove all the rivets, that hold the card together , strip off the cloth, then spray upholsterers adhesive to refit.