Do societies have a population-size limit on technological progress?

Even with a great deal of information technology and extended lifespan, there's a limit to how far and how deep a person's expertise can go. The more complex a society (and that society's technologies), the more specialized experts become, and the more of them who are needed to maintain and improve things. With a stable population, eventually there must be a limit?

We haven't seen anything like that limit over the last century because our technological explosion has been coupled with a population explosion and extraordinary leaps in information technology. But as our population flattens out somewhere between ten & twelve billion, and as we reach the limits* of computer-augmented human understanding, are we also going to reach a limit to our scientific and technological progress?

*Yes, I think that even with practically unlimited storage & computation, there's a limit to the amount of knowledge & expertise a person can reasonably access. Even if you read a book and a few relevant papers every day. And even if you have an incredible information storage & retrieval system which can easily find and recall the document you read years ago and follow up on its sources to get into the details. Even if you're mostly indexing information rather than groking it all. Eventually, there's a limit to the size of the information pyramid you can reasonably sit on top of and use effectively.