The amount of knowledge in a field increases with every new discovery (obviously). Studying something in the field obviously takes time. Is there going to be a time when a field has so much knowledge in it, that fully studying it would take longer than life (or longer than the time a person can actually study)? What would the implications for research be? Perhaps the knowledge required to perform research would simply take too long to study, and humanity would be unable to research a field? I've heard it's impossible to be a polymath now because mathematics is just too big. Is the same going to happen to specific fields too? Are we going to be unable to further develop a field (take astrophysics for example) after we discover too much? (Perhaps a one-in-a-million years genius might be able to develop it further, but nobody else, and a field will have no regular researchers.)

Unless we get a hyper-efficient communication system (that reduces the time it takes to study a particular topic (obviously communication has an impact on how long it takes to study something)), or our brains' processing power rapidly increases, I can't really think of another way it could go if a field is continually being researched (ignoring a potential societal collapse and all that).