The answer is yes – Earth does lose some of its atmosphere to space. But our atmosphere won’t disappear completely in the near future, because most of it is bound to the Earth by the force of gravity – the same force that keeps us anchored to Earth.
Molecules in our atmosphere are constantly moving, spurred on by energizing sunlight, and some move quickly enough to escape the grip of Earth’s gravity. The escape velocity for planet Earth is a little over 11 kilometers per second – about 25 thousand miles an hour. If Earth were much less massive – say, as massive as Mars – gravity’s grip would be weaker. That’s one reason why Mars lost most of its original atmosphere. Here on Earth, not all particles are equally likely to escape. Light ones, like hydrogen and helium, typically move faster than heavier ones, like oxygen and nitrogen. That’s why light molecules are rare in our atmosphere – in contrast to their abundance in the universe at large.