Have countries replaced civilizations ?
In everyday usage, people use "civilization" to refer to two things:
Things that are civil. Often contrasted with the wild, untamed others that are uncivilized, as when a hiker lost in the woods looks up to see power lines above him and exclaims "Ah! Signs of civilization!"
The meaning you're probably talking about: a culture with some degree of government, distinct art, a language we know something about, stratified society and notably separation from another group, e.g. the Egyptian Civilization, Indus River Valley Civilization, etc. Civilization usually refers to a more holistic concept than "state," "culture," "empire," or the like.
There are two main problems with using "civilization" in academic work. I'm not entirely sure what you mean by "in our times" though. If you're asking why we don't call the US and other modern states a "civilization," look at the first problem. If you're asking why we don't use the term as much as we did 100 years ago, the second problem is more relevant.
Provlem 1: I see the use of "civilization" as a short cut. If you need a quick word to say something between "Egyptian people" and the "series of dynasties that ruled the people in northeast Africa with language written in hieroglyphs and simplified versions of them and shared a surprisingly consistent culture for 2000 years" then yes, civilization will do. But how exactly do we define civilization? It can mean so many things for many groups. We say "Egyptian civilization" and "Maya civilization" as if they shared anything more than having some form of a political system and a distinct culture. But whenever there's a more accurate term, like, as you mention, "country," it's best to use that instead. Sure, I could call the USA a "civilization," but country would tell you a lot more about it. Likewise, I myself would refer to the "Maya city states," but if you're not keen on ancient Mesoamerican political organization, civilization will have to do.
Problem 2: The word has a bad history. Allow me to introduce Lewis Henry Morgan. He was, by trade, an American lawyer in the mid 19th century. If it weren't for him, anthropology as we know it wouldn't exist. That being said, he had some ideas now dismissed as archaic and probably unknowingly racist. He had a book Ancient Society that laid out what we now call "social evolutionary theory." He was that the Europeans had their Stone-Iron-Bronze age system, so he wanted something similar for the Americas. He described a sequence along which cultures developed, much like animals as one follows a phylogenic tree. Societies began in the Savagery stage, then advanced to Barabarism, and the into Civilization. Each step was marked by key technological advancements:
Savagery had fire, worship of natural things, and language
A group reached Barabarism when it discovered domestication, agriculture, and conjoined architecture
Civilization meant cultures with writing, plows, etc.
Now this isn't too bad on its own, but the details he worked in were clearly Western. For instance, a phonetic alphabet was necessary for "civilization." He then classified extant and ancient peoples into each category. Many native groups at the term were then deemed as "less socially evolved" and were not just different cultures who had adapted uniquely to their environment, but societies that represented what "civilizations" once were.