I realize this is almost an inherently unanswerable question, given that we don't know what what we don't know, and we don't know what we may eventually uncover that could radically change our perception of any given time period - but, as it stands now, are there any periods in, say, Roman history, or Chinese history, or any history, in which there's essentially nothing left to be gleaned from the sources and archaeology we have available to us, and we feel like we've got a firm and accurate grasp on?
I answered a similar, but more specific question about this kind of thing the other day here.
The long and short of it is that history is not just about collecting facts. The discipline of history is an ongoing dialog between past and present and it is heavily informed by theoretical and methodological directions and approaches. New, valuable works of history are written all the time that have only modest amounts of new "facts", but contribute to the study of the topic by approaching it from a different perspective. In point of fact, if you are a historian at a conference and someone asks you what is interesting about your work and you answer "no one has done it before" that's considered kind of a cop out answer. What should be interesting is your approach, your argument, your interpretation. It does likely include new research, but by itself that doesn't really mean all that much. Knowledge is a broad enough idea that it doesn't just include the historical "facts" that we have gathered, and there is essentially always something new to be said. That does not mean that everything new that is said ends up actually being interesting or valuable to the profession/field, but it does mean that in principle things are up for discussion in pretty much every field.
In other words, we are basically never going to be "done" with history.
Notwithstanding what other people are saying about the job of a historian, there are definitely areas where all the sources have been looked at again, and again, and again, and again, where it is highly unlikely that anything new could be said about it in a way interesting enough to warrant launching a career on it. I have known grad students who had wanted to work on certain areas--say, the early Crusades or early medieval Scandinavia--who were told not to by their advisors. The reason is that these areas have already had a disproportionately high amount of work done on them for the available sources, and it's unlikely that any new detail can be dragged out. Basically, unless you have found new sources or want to revise older work based on a new approach (one that would significantly add to our understanding of a source), then the work isn't significant enough to make a meaningful contribution to the historiography.
This isn't to say that an established historian couldn't write a one-off article on, say, the crusades, and shed new light on the subject. It just means that there probably isn't a lot of room left for yet another 500 page dissertation on the First Crusade.
I would say "no". I will give you an example why from my work as an archaeologist.
One of the first digs I was on was a Roman site in Germany. The site was something called a "Gutshof" in German, sort of a fortified farming estate that incorporates some facilities for passing travelers. The completion of this project took about 6 years, although I was only present for part of it. It was the 7th or 8th Gutshof excavated in Germany (or some similar low number, less than the 10th). The project director told me there were over 100 more known but unexcavated Gutshofs in Germany, due to lack of time, funds, or imminent threats to the sites.
So. Just in terms of rural Roman life in Gutshofs on the German frontier, we have processed something like 10% of the data, possibly less depending on how many undiscovered sites there are. Of course, not every site is going to reveal groundbreaking information, but there is always the chance to discover something new and different that expands our understanding. At this particular site we found some evidence for a previously unsuspected degree of syncretism between Roman and Germanic religious practice on the frontier.