To give up on you, I'd have to have had trust in you at some point. [The snark is automatic, even though he does actually think that Scrad and Charlie are the sort who might indeed graduate.]

But as far as Drake goes, again, I cite Arthas. Who has been here for four years and yet Drake was still convinced of his "inner goodness" and ability to graduate. Unless you're more hopelessly irredeemable than a mass murdering zombie lord, which I doubt, I find it hard to believe that Drake simply gave up.