So long as there's still one speaker of a language alive, it can still be saved for very little cost: you don't need to worry about teaching it to a new generation. Concentrate on collecting as much of it as possible and get it in audio form with translations.
Artificial intelligence will in the future be able to learn the language from these recordings (so long as you have managed to gather enough material) and it will be able to bring up future generations to speak it as native speakers if the attitude of a community changes and they decide they want their language back. In the future we're going to have talking teddies that hold fully logical conversations, and it'll be possible for all children to grow up speaking many languages automatically and without effort, all taught to them by their furry friends.
Every language is a cultural treasure and we must never just give up and let any of them die out without trying to collect them to preserve them for the future. With each language that disappears, we may be losing vital evidence as to how languages evolved from each other and of the ancient languages from which they originated.
If you're in a position to help save a language, please help to gather the data.