Yeasts are living organisms, they do not evaporate. However it is true that in most fermented food we eat, yeast are no longer there. So why is it so?
It is not the reaction with sugar and warm water that makes them disappear. Most of the time they get killed later in the food making process. For instance, if you consider yeasts in bread, like french baguette for instance, after the dough raised, it goes to the oven where yeasts cells get heat killed.
For other processes, like brewering, yeasts used to stay in the final product. But then you had to drink it before it got spoiled by yeasts that were consuming all the sugar. So nowadays, industrially produced beers are filtered or pasteurized, or both, in order to get rid of the yeasts. Only artisanal beers are still "alive", with living yeasts in it.
* * *
EDIT: As for the question "why/how do yeasts react with sugar?", sugar is actually fuel for yeasts. Yeasts oxidize sugar into CO2 in order to gain energy for their metabolism.