At this point it seems to be a result of quantum indeterminacy. In other words, since the Heisenberg uncertainty principle is in effect at that level, all we can determine is probability (hence a predictable half-life), and not specifics of events. So, it really comes down to whether or not you believe quantum mechanics. I do, and so I say no, we will not be able to determine it fully. However, many say that QM is incorrect, and so if they’re right, then yes, it is deterministic and we will (hopefully) one day be able to understand it as such.