I'm convinced that deterministic AI will never fully replicate human intelligence. I will attempt to explain my reasoning.
I can say with absolute certainty that I have subjective experience. If my behaviour is deterministic, I can imagine a philosophical zombie version of me that behaves the same but doesn't have subjective experience. That zombie, using the exact same reasoning as me, down to individual particle interactions, will (incorrectly) determine with absolute certainty that it has subjective experience and is not a philosophical zombie. Its reasoning, which is my reasoning, is thus flawed. Therefore, in order to believe my behaviour is deterministic, I must doubt my ability to reason.
(Some claim that philosophical zombies aren't possible to imagine. But I can imagine them, so if that's impossible then my reasoning is still flawed just for a different reason.)
I believe the same argument applies even if I assume my behaviour is non-deterministic but follows a probability distribution which is a function of the past -- the philosophical zombie has the same probability of reasoning that it has subjective experience as I do, and the rest of the argument is similar. Thus, I believe my behaviour is not only non-deterministic, but mathematically ineffable, and thus outside the realm of what computers can do.
If you have subjective experience which works similar to mine, maybe you can follow my reasoning. If you don't, the argument may appear to be nonsense due to the ineffability of subjective experience.