Do you mean situation in USA or all over the world?
Probably especially in the US, but elsewhere as well. Less so in some places with a strong tradition like Germany, but in decline even there. Historical Linguistics (and originally work on Indo-European of course) is really the origin of modern Linguistics in general-- from William Jones's initial popularization of comparative studies to research by Rask, Grimm, etc., and up until the 1900s, the main questions and methodologies in Linguistics were motivated by historical (usually Indo-European) questions. From there, synchronic theoretical approaches took off-- things like figuring out how phonology works in the mind of a speaker, with phonemes, etc., rather than how sounds change over time. And then Generativism with syntax trees and so forth, and then now the turn toward experimental work. Historical Linguistics has, in that sense, been becoming less central for over 100 years, but for most of that time in parallel to the new(er) research rather than being replaced by it. But today, there are fewer and fewer historical linguists, and fewer experts in the field (most today are older professors, not so many new grad students, etc., though there are still a few). I'd say that biggest factor today is the turn toward experimental/laboratory research. An oversimplified explanation would be that if the research involves statistics, it's becoming more popular, and if it doesn't, it's becoming less popular (not only, but especially, Historical Linguistics). In fact, we see that trend with some of the sometimes-nonsensical "big data" publications in Historical Linguistics today, making far-fetched claims that just don't line up with what historical linguists have known for over a century. (E.g., 'big data' research making 'innovative' claims about the Indo-European homeland. I'll add just that I don't think the methodology is "bad" per se, but that it needs to be done as an extension of, rather than alternative to, serious, well-informed Historical Linguistics, which is why I mentioned getting a background in computer science above.)
Does it mean that there's nothing to research in Indo-European linguistics?
Well, that's part of it too. If you go into Historical Linguistics, there is certainly more to be done in other parts of the world. Overall, most of the big (and "answerable") questions about Indo-European (and some other families) have already been answered. It's unclear whether we'll ever really identify the homeland or be able to decide between hypotheses for earlier relationships (Nostratic, Eurasiatic, Indo-Ugric, etc.). There is still of course a lot of research to be done on individual languages, and it continues to be published. The field is far from dead, but it's less popular now.
Do you want to say it is dead field? Sounds sad..
No, not dead. But in decline (or declined). Some of it makes sense: a lot of good research has already bee done, and now there are other questions we can ask. But the almost abandonment of Historical Linguistics
is sad. I've worked with a well known Indo-Europeanist and he has talked several times (often informally, at department seminars, etc., but also at conferences) about how Historical Linguistics is now being neglected, and sometimes this allows for bad research to surface in its place (e.g., odd claims about homelands, etc.).
I won't forget my first week of grad school when I was walking with a group of classmates and one complained to the rest of us about our Historical Linguistics class. She was apparently indignant that she had to take
one class in grad school. Odd, too, because her concentration was in phonetics, which traditionally comes out of historical research. But to me, that was very telling: at the very least, Historical Linguistics is "half" of the research that can be done (every synchronic question can be asked diachronically!-- in fact, it's even more than that-- there are about 6,000 languages around now, and there have been many, many more historically, although of course we don't have access to most of the data, but we can look at languages as they change now, and dialects, etc.). So in the end, there is a general lack of interest, some of the "big" questions have been answered, and other methodologies/subfields are becoming more popular (experimental work, etc.).
Personally, I would also comment that there is a push these days for grad students to become experts in methodologies and become very specialized, rather than learning languages first. It's simply not the case that most students start off with a strong background in Latin and Greek. That used to be the case, so it was easier to become an "Indo-Europeanist". Today, most of the research, I think, is done by narrower experts on specific (sub)families, tied into what has been done in earlier research.
