What do you think will stop artificial intelligence from becoming a closer and closer approximation of human intelligence?

The fact that our current technology (neural networks, genetic algorithms, etc.) is fundamentally different from how the human brain works. It does not have a capacity for abstract thought, emotion, creativity, etc. which are all essential to human intelligence. They can do specialized task, but we are many years away from general intelligence, and that will not come just by investing more in our current technology. If we "invent" general intelligence, it will look very different from what we have now in terms of "AI".

> our current technology (neural networks, genetic algorithms, etc.) is fundamentally different from how the human brain works.

I don't see that. Software neural networks explicitly mimic the neural networks of the human brain. Not saying there aren't functional differences, but the basic structure is there.

> It does not have a capacity for abstract thought

But 'it' does have capacity for unsupervised cluster recognition, and can use the identified clusters to influence processing results. More is likely required, but this seems to be the basic mechanism required for "abstraction."

> that will not come just by investing more in our current technology

I think you are saying that some fundamentals are still missing. I don't disagree, but we seem to have some important building blocks in hand. However, it may be the case that all the fundamentals are now in hand, and it is exactly a process of evolutionary change to yield true AI.

> general intelligence, it will look very different from what we have now

I think this is just the traditional dismissal of "whatever has actually been achieved, that is not AI." At some point this becomes an "AI of the gaps" argument, where the gaps are ever shrinking.

Your question as asked has lots of reasonable answers, such as the fact humans aren't all that intelligent on average, and certainly not some asymptotic limit we're aiming for.

That said, AI is here to stay.

I'm sure that it's here to stay, only that it will become much less valuable in the near future. Just like how the .com bubble popping didn't cause the Internet to disappear, the ML bubble popping will not cause machine learning to go away. Instead, it will make it something ubiquitous that gets used with very little thought, removing most of the specialized job market for it.

"humans aren't all that intelligent on average"