I will depend both on the age and on the type of LBV:
The older the LBV, the sooner it'll fade.
If it is a filtered LBV (most often bottled after 6 years after the Vintage, it should say so on the label) will last for a week or 2 if you store it in the fridge (think Dow, Graham, Fonseca, Taylor...). Unfiltered / traditional LBVs (bottled after 4 years, and usually closed with a proper cork) won't last that long, but as they are IMHO much more tasty as well, you won\t have a problem finishing the bottle quickly! Some houses that make Traditional LBV: Warre, Noval, Niepoort, Smith Woodhouse, Ramos Pinto. Hope this helps!