Measures can be taken to make sure languages do not become extinct. If people make an effort to keep speaking languages and preserving them, they will last forever. There should especially be measures to make sure that younger generations learn these languages so that they will continue to be spoken in the future.
When it comes to the extinction of languages, I personally think it can remain avoidable for many years to come. There are tons of countries out there, who live different cultures, and obviously speak different languages. I think it would be a very boring world if everyone spoke the same language.
So, a language is a tool used by humanity to communicate with each other. If you look at Rome and Greece, both language is considered a dead language, because of it's lack of native speaker. Everything with a start will have an end, even if it last for thousands or millions of years, don't expect it to live on for to long.
No, the extinction of languages is not avoidable, because people move and change over time. People cannot be forced to speak a certain language. As communication improves around the world, it becomes practical for people to speak the same languages. Languages should be preserved for historical purposes, but no person should be forced to speak a certain language just for the sake of it.
There will not be a universal language for humanity; even if one language were spoken worldwide, dialects amongst billions of people geographically separated would not be the same (look at Brazilian Portuguese or Okinawan Japanese). Still, regardless of the inevitable survival of multiple languages, many(or most) will die off in the near future.
Sadly, it's not possible to save all languages. There are various reasons. One is that people who speak a common language may die out. Other languages are replaced by different languages. This is what happened to some Native American languages. Latin is even essentially a "dead" language, though it's still used for some functions (like scientific terms). Additionally, languages are always evolving. The English we speak today is quite different than Old English.