How long something persists in the atmosphere once it's there depends, obviously, on how it gets removed from the atmosphere and also if anything is adding it to the atmosphere. However Different things we might consider pollutants will have different lifetimes, often very different, and it's confusing to lump them together as 'pollution'.
However there is a very important distinction to be made:
So, now, how lon things persist in the atmosphere depends on what they are: the term 'pollution' bundles together things which have radically different characteristics.