Why do some aerosol particles never settle down?

As aerosol particles get smaller, their small inertia makes them susceptible to molecular collisions with the fluid particles surrounding them—leading to the aerosol particles undergoing Brownian motion as well as any other physical effects you'd expect (like gravitational acceleration, quasi-Stokes drag, etc.) When particles are "sufficiently" small, the effects causing Brownian motion dominate, leading the aerosol particle to mostly wander around in place rather than accelerate downwards.

However—if this was the whole picture, then any aerosol would (on average) eventually settle after a sufficiently long period of time. However, in most settings, we also find macroscale fluctuations in the fluid as a result of external movement or random density changes, which cause short macroscale flows that "lift" the particle up and make settling even more difficult.