Chemistry is fun! Nothing is actually going away at all what you are observing is the transformation of nitrogenous waste products. Ammonia is released by decomposition and digestion (leftover food and fish poop). The ammonia is then eaten by a bacteria. The bacteria spits that same nitrogen out as Nitrite. Then a different bacteria eats the nitrite and spits out nitrate.
So under most circumstances (I dislike absolutes like all and none) you will have ammonia drop and nitrites rise. Then the nitrites will drop and nitrates will rise. Fairly standard is the assumption that when ammonia measured at 4 ppm is converted completely to nitrate within 24 hours, the cycle is complete enough to add fish. Slowly.