If a 1 screw case won't hold it, you could always go to the 4 screw cases. There's no recessed area, but it will keep the card in perfect condition. I've got a few of those as well, and they work just fine.
EDIT: I just realized it's an autograph card. 4 screw case might not be the answer there as it could possibly smudge the autograph. Forget that last suggestion.
Yes doctor, I am sick.
Sick of those who are spineless.
Sick of those who feel self-entitled.
Sick of those who are hypocrites.
Yes doctor, an army is forming.
Yes doctor, there will be a war.
Yes doctor, there will be blood.....