Yoiu can demonstrate a "positive" (ie, to show taht Mt. Everest is climbable, you climb it). A failure to demonstrate a positive is not a refutation of it (ie, if I set out to demonstrate that Mt. Everest is climbable and fail, it's not a proof that Mt. Everest is unclimbable, it's merelky a proof that I failed at that time).
We cannot prove that psychic phenomena exist, we can merely look at the failure to demonstrate them. We can (in theory) disprove the rather appealing hypothesis "psychic phenomena do not exist", by the simple expedient of demonstrating the converse.