An appropriately enough, threefold answer.
Material: First, the testing procedures he uses are often so stringent and allow so little leeway for incredibly minor things, even things that are utterly unrelated to the test, that the tests themselves are designed for failure. Like the most recent one from 2008, the psychometrist in question wanted obeservers to be able to film him and for them to be able to record his successes. They agreed but stipulated that if his observers, in another room, had to go to the bathroom the test would stop and their time in the bathroom counted against his overall time limit for the test. Randi's group has zero motivation for wanting to pay out a million dollars and they have already decided that the "supernatural" does not exist.
Political/Psychological: As I indicate above they have a strong motive for wanting the test subjects to fail. Not just for the money but also for their own agenda of proving everyone who believes in magic, psychic ability, god(s), sprits and the like are idiots. They have chosen as their "religion" (essentially) an anti-supernatural atheism. They will use every dirty trick and overly complex rules for their tests to ensure failure because not only does their livlihood depend on the failure of the supernatural, their entire worldview and philosophy depend on it.
Spiritual: The final reason. As I said, the determined skeptical atheist has essentially adopted "atheism" as a religion. I know, it's not a religion according to them, however the ultimate truth is that it is an unknowable and so there is no "right" answer, so by vehemently denying everyone else, they have taken a side and thus follow a religon with the same fervancy of any zealot. In my own view of "how magic works" all magic is predicated on faith and belief. Magic all stems from "the source" (or whatever you want to call it) which is basically god or the force or whatever other name you want to assign it. So, in my view, we all draw from the same infinie well of energy. Which means that those who have strong doubt, true faith and devotion in their disbelief, are drawing on the same power and are in essence "counterspelling" or giving "bad vibes" to counter and oppose their test subjects. Since Randi is stacking the odds by having multiple members of his team against what is usually a single participant, it is an unfair battle of wills.
These three factors converge to create virtually unbeatable and extremely hostile testing environment. When you factor in that so much magical work takes place on the astral or invisible to the naked eye or in subtle ways that can't be recorded he has created a wonderful scheme for getting donations and gathering "proof" that the supernatural doesn't exist.
I do not believe he would accept any measure of proof as fact. He has chosen disbelief and has created an unwinnable challenge for the purposes of furthering his own agenda and grinding his own personal axe.