How long is fresh yeast good stay good for?

If it's one of those cubes from companies like Fleischmann's or Red Star, then you'll be able to see a "best by" date imprinted on the package. If not, a few weeks-- like 2-3 weeks, if you keep it in ideal conditions. That means, keep it refrigerated and wrapped in foil or plastic wrap so it's protected from air. Fresh yeast is far more delicate than instant yeast or active yeast.

Even after the expiration date, it will like work. But, it just won't be as potent.

I would be careful with fresh yeast as depending on the manufacturer it may or may not have a date on it. There are a few ways to tell if your yeast has gone bad. When you first buy yeast it should be a tan/ skin color. As it dries out it will lose that color and begin to loose its moisture turning more of a whitish powdery color and texture. If the yeast isn't held in a dry container or wrapped and moisture gets in it will actually begin to mold. If when you try and dissolve the yeast in warm water and it does not dissolve or bubble it is most likely dead.
Like Raj said in the last response, fresh yeast if stored properly should last 2-3 weeks