Not as often as macroscopic objects do. Gravity takes time to build the velocity of an object, and if there isn’t sufficient distance it will still be travelling quite slowly when it hits the ground. The electromagnetic force which holds everything together on every scale between the atomic and galactic scales is also much stronger in a relative sense for small objects, so the object wouldn’t be as fragile.
Volume and mass for a typical object scales with the cube of a length while surface scales with the square. This means that as that length becomes smaller, the ratio of the surface area to the mass increases, making forces that arise from surface effects stronger relative to gravity. This is why ants fall rather slowly and dust particles can be suspended in air for long periods of time.
What @hiphiphopflipflapflop said, in simpler terms, is that gravity acts less strongly as things get smaller. That’s why when you drop a bug out a one-story window, it’ll be totally fine. If you drop a cat from the same distance, it’ll be really upset but probably ok. You drop an elephant those same ~ten feet? It’ll probably break some bones, maybe die.