The basis of their belief is the supernatural. The supernatural doesn't require anything other than their belief to support it. Lets say you successfully attack one belief. Another belief can easily appear in it's place. For example, used to be all non-believers go to eternal hell. You point out how unfair this is. So hell now becomes a temporary place, or you, the non-believer misunderstood the meaning of hell.
While I've used the same argument myself for my lack of belief, I find most believers feel that God has somehow influenced their life which wouldn't be the same if God didn't exist. Signs is a big one. Something happens, they see it as a sign from God. They base a decision on this sign. They feel their life has improved because of the sign God sent which they listen to. Without the sign they would have made a different decision which would, of course, made their life worse.
Since you can't have them go back in time to have them make a different decision, you can't prove otherwise.