Even with continuous backpropagation and "learning", enriching the training data, so called online-learning, the limitations will not disappear. The LLMs will not be able to conclude things about the world based on fact and deduction. They only consider what is likely from their training data. They will not foresee/anticipate events, that are unlikely or non-existent in their training data, but are bound to happen due to real world circumstances. They are not intelligent in that way.
Whether humans always apply that much effort to conclude these things is another question. The point is, that humans fundamentally are capable of doing that, while LLMs are structurally not.
The problems are structural/architectural. I think it will take another 2-3 major leaps in architectures, before these AI models reach human level general intelligence, if they ever reach it. So far they can "merely" often "fake it" when things are statistically common in their training data.